gap> RequirePackage("grape"); Loading GRAPE 4.0 (GRaph Algorithms using PErmutation groups), by L.H.Soicher@qmw.ac.uk. true gap> gap> n:=3;; # projective dimension (>2) gap> q:=4;; # field size gap> gap> F:=GaloisField(q);; gap> G:=GL(n+1,q);; gap> zerovector:=ListWithIdenticalEntries(n+1,Zero(F));; gap> p1:=ShallowCopy(zerovector);; gap> p1[1]:=One(F);; gap> p2:=ShallowCopy(zerovector);; gap> p2[2]:=One(F);; gap> projectiveline:=Union([p2],List(Elements(F),x->p1+x*p2));; gap> gap> readableFFE := function(F,x) > # > # Returns an object to print for the element x of the finite field F, > # for easy human reading when x is in the prime subfield of F. > # > if x in PrimeField(F) then > return IntFFE(x); > else > return x; > fi; > end; function( F, x ) ... end gap> gap> OnProjectivePointSets := function(projpointset,g) > # > # returns the image of projective point set projpointset under the matrix g. > # > return Set(List(projpointset,x->OnLines(x,g))); > # Note: In GAP, a *line* is what we would call a representative of > # a projective point. > end; function( projpointset, g ) ... end gap> gap> gamma:=Graph(G, > Set(Orbit(G,projectiveline,OnProjectivePointSets)), > OnProjectivePointSets, > function(x,y) > # adjacency relation: join iff x and y are disjoint. > return Intersection(x,y)=[]; > end, > true);; gap> gap> # Display information about gamma. gap> OrderGraph(gamma); 357 gap> GlobalParameters(gamma); [ [ 0, 0, 256 ], [ 1, 180, 75 ], [ 192, 64, 0 ] ] gap> Size(gamma.group); 987033600 gap> gap> Runtime(); 7400 gap> maxcliques:=CompleteSubgraphs(gamma);; gap> # gap> # maxcliques is now a generating set for the gamma.group-set of gap> # maximal cliques of gamma (which give the maximal partial spreads of gap> # PG(n,q)). gap> # gap> Runtime(); 1167410 gap> gap> hom:=ActionHomomorphism(G,VertexNames(gamma),OnProjectivePointSets);; gap> GG:=Image(hom);; # GG = PGL(n+1,q) acting on the vertices of gamma. gap> # gap> # Now determine GG-orbit representatives of maxcliques. gap> # gap> reps:=List([1..Maximum(List(maxcliques,Size))],x->[]);; gap> for clique in maxcliques do > # determine whether clique represents a new orbit > k:=Length(clique); > equiv:=false; > for rep in reps[k] do > if RepresentativeAction(GG,clique,rep,OnSets)<>fail then > # clique and rep are in the same GG-orbit > equiv:=true; > break; > fi; > od; > if not equiv then > AddSet(reps[k],clique); > fi; > od; gap> Runtime(); 191963820 gap> gap> maxreps:=Concatenation(reps);; gap> # gap> # Display the numbers of inequivalent maximal partial spreads of each size. gap> # gap> Collected(List(maxreps,Length)); [ [ 11, 6 ], [ 12, 3 ], [ 13, 13 ], [ 14, 4 ], [ 17, 3 ] ] gap> # gap> # Now display the representative maximal partial spreads. gap> # gap> for k in [1..Length(reps)] do > if Length(reps[k])<>0 then > Print("\n\nTHE ",Length(reps[k]), > " INEQUIVALENT MAXIMAL PARTIAL SPREAD(S) OF SIZE ", k,":\n"); > for rep in reps[k] do > Print("\nMaximal partial spread:\n",List(rep,x->List(VertexName(gamma,x), > v->List(v,y->readableFFE(F,y))))); > HH:=Stabilizer(GG,rep,OnSets); > H:=PreImage(hom,HH); > Print("\nThe stabilizer of this partial spread in PGL(",n+1,",",q,")", > " has size ",Size(HH)," and is generated by", > " the images of the matrices:\n"); > for g in GeneratorsOfGroup(H) do > Print(List(g,x->List(x,y->readableFFE(F,y))),",\n"); > od; > od; > fi; > od; THE 6 INEQUIVALENT MAXIMAL PARTIAL SPREAD(S) OF SIZE 11: Maximal partial spread: [ [ [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ], [ 0, 0, 1, 1 ], [ 0, 0, 1, Z(2^2) ], [ 0, 0, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 1, 1, 0, 0 ], [ 1, Z(2^2), 0, 0 ], [ 1, Z(2^2)^2, 0, 0 ] ], [ [ 0, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 1, 1, 1, 1 ], [ 1, Z(2^2), 1, Z(2^2) ], [ 1, Z(2^2)^2, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, Z(2^2) ], [ 1, 0, Z(2^2), 0 ], [ 1, 1, Z(2^2), Z(2^2) ], [ 1, Z(2^2), Z(2^2), Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2), 1 ] ], [ [ 0, 1, 0, Z(2^2)^2 ], [ 1, 0, Z(2^2)^2, 0 ], [ 1, 1, Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2), Z(2^2)^2, 1 ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2) ] ], [ [ 0, 1, 1, 0 ], [ 1, 0, 1, Z(2^2) ], [ 1, 1, 0, Z(2^2) ], [ 1, Z(2^2), Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2)^2, Z(2^2), Z(2^2) ] ], [ [ 0, 1, 1, 1 ], [ 1, 0, Z(2^2)^2, 1 ], [ 1, 1, Z(2^2), 0 ], [ 1, Z(2^2), 1, Z(2^2)^2 ], [ 1, Z(2^2)^2, 0, Z(2^2) ] ], [ [ 0, 1, 1, Z(2^2)^2 ], [ 1, 0, 0, 1 ], [ 1, 1, 1, Z(2^2) ], [ 1, Z(2^2), Z(2^2), 0 ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2)^2 ] ], [ [ 0, 1, Z(2^2)^2, 0 ], [ 1, 0, 1, 1 ], [ 1, 1, Z(2^2), 1 ], [ 1, Z(2^2), 0, 1 ], [ 1, Z(2^2)^2, Z(2^2)^2, 1 ] ], [ [ 0, 1, Z(2^2)^2, 1 ], [ 1, 0, Z(2^2), Z(2^2) ], [ 1, 1, 1, Z(2^2)^2 ], [ 1, Z(2^2), Z(2^2)^2, 0 ], [ 1, Z(2^2)^2, 0, 1 ] ], [ [ 0, 1, Z(2^2)^2, Z(2^2) ], [ 1, 0, 0, Z(2^2) ], [ 1, 1, Z(2^2)^2, 0 ], [ 1, Z(2^2), 1, 1 ], [ 1, Z(2^2)^2, Z(2^2), Z(2^2)^2 ] ] ] The stabilizer of this partial spread in PGL(4,4) has size 60 and is generated by the images of the matrices: [ [ Z(2^2)^2, 0, 0, 0 ], [ 0, Z(2^2)^2, 0, 0 ], [ 0, 0, Z(2^2)^2, 0 ], [ 0, 0, 0, Z(2^2)^2 ] ], [ [ Z(2^2), Z(2^2), Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2), Z(2^2), Z(2^2)^2 ], [ 0, 0, Z(2^2), Z(2^2) ], [ 0, 0, 1, Z(2^2) ] ], [ [ 0, 1, 0, 1 ], [ 1, 1, 1, 1 ], [ 0, 0, 0, Z(2^2)^2 ], [ 0, 0, Z(2^2)^2, Z(2^2)^2 ] ], [ [ 1, 1, Z(2^2), Z(2^2) ], [ 0, Z(2^2), 0, Z(2^2)^2 ], [ Z(2^2)^2, Z(2^2)^2, 0, 0 ], [ 0, 1, 0, 0 ] ], Maximal partial spread: [ [ [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ], [ 0, 0, 1, 1 ], [ 0, 0, 1, Z(2^2) ], [ 0, 0, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 1, 1, 0, 0 ], [ 1, Z(2^2), 0, 0 ], [ 1, Z(2^2)^2, 0, 0 ] ], [ [ 0, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 1, 1, 1, 1 ], [ 1, Z(2^2), 1, Z(2^2) ], [ 1, Z(2^2)^2, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, Z(2^2) ], [ 1, 0, Z(2^2), 0 ], [ 1, 1, Z(2^2), Z(2^2) ], [ 1, Z(2^2), Z(2^2), Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2), 1 ] ], [ [ 0, 1, 0, Z(2^2)^2 ], [ 1, 0, Z(2^2)^2, 0 ], [ 1, 1, Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2), Z(2^2)^2, 1 ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2) ] ], [ [ 0, 1, 1, 0 ], [ 1, 0, 1, Z(2^2) ], [ 1, 1, 0, Z(2^2) ], [ 1, Z(2^2), Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2)^2, Z(2^2), Z(2^2) ] ], [ [ 0, 1, 1, 1 ], [ 1, 0, Z(2^2)^2, 1 ], [ 1, 1, Z(2^2), 0 ], [ 1, Z(2^2), 1, Z(2^2)^2 ], [ 1, Z(2^2)^2, 0, Z(2^2) ] ], [ [ 0, 1, 1, Z(2^2)^2 ], [ 1, 0, 0, Z(2^2)^2 ], [ 1, 1, 1, 0 ], [ 1, Z(2^2), Z(2^2), Z(2^2) ], [ 1, Z(2^2)^2, Z(2^2)^2, 1 ] ], [ [ 0, 1, Z(2^2), 0 ], [ 1, 0, Z(2^2)^2, Z(2^2)^2 ], [ 1, 1, 1, Z(2^2)^2 ], [ 1, Z(2^2), 0, Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2), Z(2^2)^2 ] ], [ [ 0, 1, Z(2^2), 1 ], [ 1, 0, 0, Z(2^2) ], [ 1, 1, Z(2^2), Z(2^2)^2 ], [ 1, Z(2^2), Z(2^2)^2, 0 ], [ 1, Z(2^2)^2, 1, 1 ] ], [ [ 0, 1, Z(2^2), Z(2^2)^2 ], [ 1, 0, 1, 1 ], [ 1, 1, Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2), Z(2^2), 0 ], [ 1, Z(2^2)^2, 0, Z(2^2)^2 ] ] ] The stabilizer of this partial spread in PGL(4,4) has size 60 and is generated by the images of the matrices: [ [ Z(2^2)^2, 0, 0, 0 ], [ 0, Z(2^2)^2, 0, 0 ], [ 0, 0, Z(2^2)^2, 0 ], [ 0, 0, 0, Z(2^2)^2 ] ], [ [ Z(2^2)^2, 0, 1, 0 ], [ 1, Z(2^2)^2, Z(2^2), 1 ], [ 0, 0, Z(2^2)^2, 0 ], [ 0, 0, 1, Z(2^2)^2 ] ], [ [ Z(2^2), 0, Z(2^2), 0 ], [ Z(2^2), 1, Z(2^2), 1 ], [ 0, 0, 1, 0 ], [ 0, 0, 1, Z(2^2)^2 ] ], [ [ 0, 0, Z(2^2), 1 ], [ 0, 0, 0, Z(2^2) ], [ Z(2^2)^2, Z(2^2), 0, 0 ], [ 0, Z(2^2)^2, 0, 0 ] ], Maximal partial spread: [ [ [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ], [ 0, 0, 1, 1 ], [ 0, 0, 1, Z(2^2) ], [ 0, 0, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 1, 1, 0, 0 ], [ 1, Z(2^2), 0, 0 ], [ 1, Z(2^2)^2, 0, 0 ] ], [ [ 0, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 1, 1, 1, 1 ], [ 1, Z(2^2), 1, Z(2^2) ], [ 1, Z(2^2)^2, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, Z(2^2) ], [ 1, 0, Z(2^2), 0 ], [ 1, 1, Z(2^2), Z(2^2) ], [ 1, Z(2^2), Z(2^2), Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2), 1 ] ], [ [ 0, 1, 0, Z(2^2)^2 ], [ 1, 0, Z(2^2)^2, 1 ], [ 1, 1, Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2), Z(2^2)^2, 0 ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2)^2 ] ], [ [ 0, 1, 1, 0 ], [ 1, 0, 0, Z(2^2) ], [ 1, 1, 1, Z(2^2) ], [ 1, Z(2^2), Z(2^2), Z(2^2) ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2) ] ], [ [ 0, 1, Z(2^2), 0 ], [ 1, 0, Z(2^2), 1 ], [ 1, 1, 0, 1 ], [ 1, Z(2^2), 1, 1 ], [ 1, Z(2^2)^2, Z(2^2)^2, 1 ] ], [ [ 0, 1, Z(2^2), 1 ], [ 1, 0, 0, 1 ], [ 1, 1, Z(2^2), 0 ], [ 1, Z(2^2), Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2)^2, 1, Z(2^2) ] ], [ [ 0, 1, Z(2^2), Z(2^2) ], [ 1, 0, Z(2^2)^2, Z(2^2) ], [ 1, 1, 1, 0 ], [ 1, Z(2^2), 0, 1 ], [ 1, Z(2^2)^2, Z(2^2), Z(2^2)^2 ] ], [ [ 0, 1, Z(2^2)^2, 1 ], [ 1, 0, Z(2^2)^2, Z(2^2)^2 ], [ 1, 1, 0, Z(2^2) ], [ 1, Z(2^2), Z(2^2), 1 ], [ 1, Z(2^2)^2, 1, 0 ] ], [ [ 0, 1, Z(2^2)^2, Z(2^2) ], [ 1, 0, 1, 1 ], [ 1, 1, Z(2^2), Z(2^2)^2 ], [ 1, Z(2^2), 0, Z(2^2) ], [ 1, Z(2^2)^2, Z(2^2)^2, 0 ] ] ] The stabilizer of this partial spread in PGL(4,4) has size 3 and is generated by the images of the matrices: [ [ Z(2^2)^2, 0, 0, 0 ], [ 0, Z(2^2)^2, 0, 0 ], [ 0, 0, Z(2^2)^2, 0 ], [ 0, 0, 0, Z(2^2)^2 ] ], [ [ Z(2^2), 0, 1, 1 ], [ Z(2^2)^2, Z(2^2), Z(2^2)^2, 0 ], [ Z(2^2), 1, 1, 1 ], [ 1, Z(2^2), Z(2^2)^2, 0 ] ], Maximal partial spread: [ [ [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ], [ 0, 0, 1, 1 ], [ 0, 0, 1, Z(2^2) ], [ 0, 0, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 1, 1, 0, 0 ], [ 1, Z(2^2), 0, 0 ], [ 1, Z(2^2)^2, 0, 0 ] ], [ [ 0, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 1, 1, 1, 1 ], [ 1, Z(2^2), 1, Z(2^2) ], [ 1, Z(2^2)^2, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, Z(2^2) ], [ 1, 0, Z(2^2), 0 ], [ 1, 1, Z(2^2), Z(2^2) ], [ 1, Z(2^2), Z(2^2), Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2), 1 ] ], [ [ 0, 1, 0, Z(2^2)^2 ], [ 1, 0, Z(2^2)^2, 1 ], [ 1, 1, Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2), Z(2^2)^2, 0 ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2)^2 ] ], [ [ 0, 1, 1, 0 ], [ 1, 0, 0, Z(2^2) ], [ 1, 1, 1, Z(2^2) ], [ 1, Z(2^2), Z(2^2), Z(2^2) ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2) ] ], [ [ 0, 1, Z(2^2), 0 ], [ 1, 0, Z(2^2), 1 ], [ 1, 1, 0, 1 ], [ 1, Z(2^2), 1, 1 ], [ 1, Z(2^2)^2, Z(2^2)^2, 1 ] ], [ [ 0, 1, Z(2^2), 1 ], [ 1, 0, 1, Z(2^2) ], [ 1, 1, Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2), Z(2^2), 0 ], [ 1, Z(2^2)^2, 0, 1 ] ], [ [ 0, 1, Z(2^2), Z(2^2)^2 ], [ 1, 0, 0, Z(2^2)^2 ], [ 1, 1, Z(2^2), 0 ], [ 1, Z(2^2), Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2)^2, 1, 1 ] ], [ [ 0, 1, Z(2^2)^2, 1 ], [ 1, 0, Z(2^2)^2, Z(2^2)^2 ], [ 1, 1, 0, Z(2^2) ], [ 1, Z(2^2), Z(2^2), 1 ], [ 1, Z(2^2)^2, 1, 0 ] ], [ [ 0, 1, Z(2^2)^2, Z(2^2) ], [ 1, 0, Z(2^2), Z(2^2) ], [ 1, 1, 1, 0 ], [ 1, Z(2^2), Z(2^2)^2, 1 ], [ 1, Z(2^2)^2, 0, Z(2^2)^2 ] ] ] The stabilizer of this partial spread in PGL(4,4) has size 3 and is generated by the images of the matrices: [ [ Z(2^2)^2, 0, 0, 0 ], [ 0, Z(2^2)^2, 0, 0 ], [ 0, 0, Z(2^2)^2, 0 ], [ 0, 0, 0, Z(2^2)^2 ] ], [ [ Z(2^2)^2, 0, 0, 0 ], [ 0, Z(2^2), 0, 0 ], [ Z(2^2), 0, Z(2^2), 0 ], [ 0, 1, 0, 1 ] ], Maximal partial spread: [ [ [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ], [ 0, 0, 1, 1 ], [ 0, 0, 1, Z(2^2) ], [ 0, 0, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 1, 1, 0, 0 ], [ 1, Z(2^2), 0, 0 ], [ 1, Z(2^2)^2, 0, 0 ] ], [ [ 0, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 1, 1, 1, 1 ], [ 1, Z(2^2), 1, Z(2^2) ], [ 1, Z(2^2)^2, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, Z(2^2) ], [ 1, 0, Z(2^2), 0 ], [ 1, 1, Z(2^2), Z(2^2) ], [ 1, Z(2^2), Z(2^2), Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2), 1 ] ], [ [ 0, 1, 0, Z(2^2)^2 ], [ 1, 0, Z(2^2)^2, 1 ], [ 1, 1, Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2), Z(2^2)^2, 0 ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2)^2 ] ], [ [ 0, 1, 1, 0 ], [ 1, 0, 0, Z(2^2) ], [ 1, 1, 1, Z(2^2) ], [ 1, Z(2^2), Z(2^2), Z(2^2) ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2) ] ], [ [ 0, 1, Z(2^2), 0 ], [ 1, 0, Z(2^2), 1 ], [ 1, 1, 0, 1 ], [ 1, Z(2^2), 1, 1 ], [ 1, Z(2^2)^2, Z(2^2)^2, 1 ] ], [ [ 0, 1, Z(2^2), 1 ], [ 1, 0, 1, Z(2^2) ], [ 1, 1, Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2), Z(2^2), 0 ], [ 1, Z(2^2)^2, 0, 1 ] ], [ [ 0, 1, Z(2^2), Z(2^2)^2 ], [ 1, 0, Z(2^2)^2, 0 ], [ 1, 1, 1, Z(2^2)^2 ], [ 1, Z(2^2), 0, 1 ], [ 1, Z(2^2)^2, Z(2^2), Z(2^2) ] ], [ [ 0, 1, Z(2^2)^2, 1 ], [ 1, 0, Z(2^2)^2, Z(2^2)^2 ], [ 1, 1, 0, Z(2^2) ], [ 1, Z(2^2), Z(2^2), 1 ], [ 1, Z(2^2)^2, 1, 0 ] ], [ [ 0, 1, Z(2^2)^2, Z(2^2) ], [ 1, 0, 1, 1 ], [ 1, 1, Z(2^2), Z(2^2)^2 ], [ 1, Z(2^2), 0, Z(2^2) ], [ 1, Z(2^2)^2, Z(2^2)^2, 0 ] ] ] The stabilizer of this partial spread in PGL(4,4) has size 3 and is generated by the images of the matrices: [ [ Z(2^2)^2, 0, 0, 0 ], [ 0, Z(2^2)^2, 0, 0 ], [ 0, 0, Z(2^2)^2, 0 ], [ 0, 0, 0, Z(2^2)^2 ] ], [ [ 0, Z(2^2)^2, 0, 0 ], [ Z(2^2), 1, 0, 0 ], [ 0, Z(2^2), 0, Z(2^2) ], [ 1, Z(2^2)^2, 1, Z(2^2)^2 ] ], Maximal partial spread: [ [ [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ], [ 0, 0, 1, 1 ], [ 0, 0, 1, Z(2^2) ], [ 0, 0, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 1, 1, 0, 0 ], [ 1, Z(2^2), 0, 0 ], [ 1, Z(2^2)^2, 0, 0 ] ], [ [ 0, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 1, 1, 1, 1 ], [ 1, Z(2^2), 1, Z(2^2) ], [ 1, Z(2^2)^2, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, Z(2^2) ], [ 1, 0, Z(2^2), 0 ], [ 1, 1, Z(2^2), Z(2^2) ], [ 1, Z(2^2), Z(2^2), Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2), 1 ] ], [ [ 0, 1, 0, Z(2^2)^2 ], [ 1, 0, Z(2^2)^2, 1 ], [ 1, 1, Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2), Z(2^2)^2, 0 ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2)^2 ] ], [ [ 0, 1, 1, 0 ], [ 1, 0, 1, Z(2^2) ], [ 1, 1, 0, Z(2^2) ], [ 1, Z(2^2), Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2)^2, Z(2^2), Z(2^2) ] ], [ [ 0, 1, 1, 1 ], [ 1, 0, 0, Z(2^2)^2 ], [ 1, 1, 1, Z(2^2) ], [ 1, Z(2^2), Z(2^2), 1 ], [ 1, Z(2^2)^2, Z(2^2)^2, 0 ] ], [ [ 0, 1, 1, Z(2^2) ], [ 1, 0, Z(2^2)^2, Z(2^2) ], [ 1, 1, Z(2^2), 0 ], [ 1, Z(2^2), 1, 1 ], [ 1, Z(2^2)^2, 0, Z(2^2)^2 ] ], [ [ 0, 1, Z(2^2), 0 ], [ 1, 0, Z(2^2)^2, Z(2^2)^2 ], [ 1, 1, 1, Z(2^2)^2 ], [ 1, Z(2^2), 0, Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2), Z(2^2)^2 ] ], [ [ 0, 1, Z(2^2), Z(2^2) ], [ 1, 0, Z(2^2), Z(2^2)^2 ], [ 1, 1, 0, 1 ], [ 1, Z(2^2), 1, 0 ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2) ] ], [ [ 0, 1, Z(2^2), Z(2^2)^2 ], [ 1, 0, 0, Z(2^2) ], [ 1, 1, Z(2^2), 1 ], [ 1, Z(2^2), Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2)^2, 1, 0 ] ] ] The stabilizer of this partial spread in PGL(4,4) has size 3 and is generated by the images of the matrices: [ [ Z(2^2)^2, 0, 0, 0 ], [ 0, Z(2^2)^2, 0, 0 ], [ 0, 0, Z(2^2)^2, 0 ], [ 0, 0, 0, Z(2^2)^2 ] ], [ [ 1, Z(2^2), Z(2^2)^2, 0 ], [ Z(2^2)^2, Z(2^2), Z(2^2), Z(2^2) ], [ 0, 1, 1, 1 ], [ Z(2^2), 0, 0, 1 ] ], THE 3 INEQUIVALENT MAXIMAL PARTIAL SPREAD(S) OF SIZE 12: Maximal partial spread: [ [ [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ], [ 0, 0, 1, 1 ], [ 0, 0, 1, Z(2^2) ], [ 0, 0, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 1, 1, 0, 0 ], [ 1, Z(2^2), 0, 0 ], [ 1, Z(2^2)^2, 0, 0 ] ], [ [ 0, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 1, 1, 1, 1 ], [ 1, Z(2^2), 1, Z(2^2) ], [ 1, Z(2^2)^2, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, Z(2^2) ], [ 1, 0, Z(2^2), 0 ], [ 1, 1, Z(2^2), Z(2^2) ], [ 1, Z(2^2), Z(2^2), Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2), 1 ] ], [ [ 0, 1, 0, Z(2^2)^2 ], [ 1, 0, Z(2^2)^2, 1 ], [ 1, 1, Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2), Z(2^2)^2, 0 ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2)^2 ] ], [ [ 0, 1, 1, 0 ], [ 1, 0, 0, Z(2^2) ], [ 1, 1, 1, Z(2^2) ], [ 1, Z(2^2), Z(2^2), Z(2^2) ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2) ] ], [ [ 0, 1, 1, 1 ], [ 1, 0, 1, Z(2^2)^2 ], [ 1, 1, 0, Z(2^2) ], [ 1, Z(2^2), Z(2^2)^2, 1 ], [ 1, Z(2^2)^2, Z(2^2), 0 ] ], [ [ 0, 1, Z(2^2), 0 ], [ 1, 0, Z(2^2), 1 ], [ 1, 1, 0, 1 ], [ 1, Z(2^2), 1, 1 ], [ 1, Z(2^2)^2, Z(2^2)^2, 1 ] ], [ [ 0, 1, Z(2^2), 1 ], [ 1, 0, 0, 1 ], [ 1, 1, Z(2^2), 0 ], [ 1, Z(2^2), Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2)^2, 1, Z(2^2) ] ], [ [ 0, 1, Z(2^2)^2, 1 ], [ 1, 0, Z(2^2)^2, Z(2^2) ], [ 1, 1, 0, Z(2^2)^2 ], [ 1, Z(2^2), Z(2^2), 0 ], [ 1, Z(2^2)^2, 1, 1 ] ], [ [ 0, 1, Z(2^2)^2, Z(2^2) ], [ 1, 0, 0, Z(2^2)^2 ], [ 1, 1, Z(2^2)^2, 1 ], [ 1, Z(2^2), 1, 0 ], [ 1, Z(2^2)^2, Z(2^2), Z(2^2) ] ], [ [ 0, 1, Z(2^2)^2, Z(2^2)^2 ], [ 1, 0, 1, Z(2^2) ], [ 1, 1, Z(2^2), 1 ], [ 1, Z(2^2), 0, Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2)^2, 0 ] ] ] The stabilizer of this partial spread in PGL(4,4) has size 4 and is generated by the images of the matrices: [ [ Z(2^2)^2, 0, 0, 0 ], [ 0, Z(2^2)^2, 0, 0 ], [ 0, 0, Z(2^2)^2, 0 ], [ 0, 0, 0, Z(2^2)^2 ] ], [ [ 0, 0, Z(2^2), Z(2^2) ], [ 0, 0, 1, Z(2^2) ], [ 1, 1, 0, 0 ], [ Z(2^2)^2, 1, 0, 0 ] ], [ [ 1, 1, 0, Z(2^2) ], [ Z(2^2)^2, 1, Z(2^2), Z(2^2)^2 ], [ Z(2^2), 1, 1, 1 ], [ 1, 0, Z(2^2)^2, 1 ] ], Maximal partial spread: [ [ [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ], [ 0, 0, 1, 1 ], [ 0, 0, 1, Z(2^2) ], [ 0, 0, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 1, 1, 0, 0 ], [ 1, Z(2^2), 0, 0 ], [ 1, Z(2^2)^2, 0, 0 ] ], [ [ 0, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 1, 1, 1, 1 ], [ 1, Z(2^2), 1, Z(2^2) ], [ 1, Z(2^2)^2, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, Z(2^2) ], [ 1, 0, Z(2^2), 0 ], [ 1, 1, Z(2^2), Z(2^2) ], [ 1, Z(2^2), Z(2^2), Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2), 1 ] ], [ [ 0, 1, 0, Z(2^2)^2 ], [ 1, 0, Z(2^2)^2, 1 ], [ 1, 1, Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2), Z(2^2)^2, 0 ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2)^2 ] ], [ [ 0, 1, 1, 0 ], [ 1, 0, 0, Z(2^2) ], [ 1, 1, 1, Z(2^2) ], [ 1, Z(2^2), Z(2^2), Z(2^2) ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2) ] ], [ [ 0, 1, Z(2^2), 0 ], [ 1, 0, Z(2^2), 1 ], [ 1, 1, 0, 1 ], [ 1, Z(2^2), 1, 1 ], [ 1, Z(2^2)^2, Z(2^2)^2, 1 ] ], [ [ 0, 1, Z(2^2), Z(2^2) ], [ 1, 0, 1, Z(2^2)^2 ], [ 1, 1, Z(2^2)^2, 1 ], [ 1, Z(2^2), Z(2^2), 0 ], [ 1, Z(2^2)^2, 0, Z(2^2) ] ], [ [ 0, 1, Z(2^2), Z(2^2)^2 ], [ 1, 0, 0, Z(2^2)^2 ], [ 1, 1, Z(2^2), 0 ], [ 1, Z(2^2), Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2)^2, 1, 1 ] ], [ [ 0, 1, Z(2^2)^2, 0 ], [ 1, 0, Z(2^2), Z(2^2)^2 ], [ 1, 1, 1, Z(2^2)^2 ], [ 1, Z(2^2), Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2)^2, 0, Z(2^2)^2 ] ], [ [ 0, 1, Z(2^2)^2, 1 ], [ 1, 0, Z(2^2)^2, Z(2^2)^2 ], [ 1, 1, 0, Z(2^2) ], [ 1, Z(2^2), Z(2^2), 1 ], [ 1, Z(2^2)^2, 1, 0 ] ], [ [ 0, 1, Z(2^2)^2, Z(2^2) ], [ 1, 0, 1, 1 ], [ 1, 1, Z(2^2), Z(2^2)^2 ], [ 1, Z(2^2), 0, Z(2^2) ], [ 1, Z(2^2)^2, Z(2^2)^2, 0 ] ] ] The stabilizer of this partial spread in PGL(4,4) has size 4 and is generated by the images of the matrices: [ [ Z(2^2)^2, 0, 0, 0 ], [ 0, Z(2^2)^2, 0, 0 ], [ 0, 0, Z(2^2)^2, 0 ], [ 0, 0, 0, Z(2^2)^2 ] ], [ [ Z(2^2)^2, Z(2^2)^2, 0, Z(2^2)^2 ], [ Z(2^2), Z(2^2)^2, Z(2^2), Z(2^2) ], [ 0, 0, 1, 1 ], [ 0, 0, Z(2^2), 1 ] ], [ [ Z(2^2), Z(2^2), Z(2^2), Z(2^2) ], [ 0, Z(2^2)^2, 0, Z(2^2)^2 ], [ 0, Z(2^2)^2, Z(2^2)^2, 0 ], [ 1, 1, 1, Z(2^2) ] ], Maximal partial spread: [ [ [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ], [ 0, 0, 1, 1 ], [ 0, 0, 1, Z(2^2) ], [ 0, 0, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 1, 1, 0, 0 ], [ 1, Z(2^2), 0, 0 ], [ 1, Z(2^2)^2, 0, 0 ] ], [ [ 0, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 1, 1, 1, 1 ], [ 1, Z(2^2), 1, Z(2^2) ], [ 1, Z(2^2)^2, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, Z(2^2) ], [ 1, 0, Z(2^2), 0 ], [ 1, 1, Z(2^2), Z(2^2) ], [ 1, Z(2^2), Z(2^2), Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2), 1 ] ], [ [ 0, 1, 0, Z(2^2)^2 ], [ 1, 0, Z(2^2)^2, 1 ], [ 1, 1, Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2), Z(2^2)^2, 0 ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2)^2 ] ], [ [ 0, 1, 1, 0 ], [ 1, 0, 1, Z(2^2) ], [ 1, 1, 0, Z(2^2) ], [ 1, Z(2^2), Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2)^2, Z(2^2), Z(2^2) ] ], [ [ 0, 1, 1, 1 ], [ 1, 0, 0, Z(2^2) ], [ 1, 1, 1, Z(2^2)^2 ], [ 1, Z(2^2), Z(2^2), 0 ], [ 1, Z(2^2)^2, Z(2^2)^2, 1 ] ], [ [ 0, 1, 1, Z(2^2) ], [ 1, 0, Z(2^2)^2, Z(2^2)^2 ], [ 1, 1, Z(2^2), 1 ], [ 1, Z(2^2), 1, 0 ], [ 1, Z(2^2)^2, 0, Z(2^2) ] ], [ [ 0, 1, Z(2^2), 1 ], [ 1, 0, 0, 1 ], [ 1, 1, Z(2^2), 0 ], [ 1, Z(2^2), Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2)^2, 1, Z(2^2) ] ], [ [ 0, 1, Z(2^2), Z(2^2)^2 ], [ 1, 0, 1, Z(2^2)^2 ], [ 1, 1, Z(2^2)^2, 0 ], [ 1, Z(2^2), Z(2^2), Z(2^2) ], [ 1, Z(2^2)^2, 0, 1 ] ], [ [ 0, 1, Z(2^2)^2, 0 ], [ 1, 0, 0, Z(2^2)^2 ], [ 1, 1, Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2), 1, Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2), Z(2^2)^2 ] ], [ [ 0, 1, Z(2^2)^2, Z(2^2) ], [ 1, 0, Z(2^2), Z(2^2) ], [ 1, 1, 1, 0 ], [ 1, Z(2^2), Z(2^2)^2, 1 ], [ 1, Z(2^2)^2, 0, Z(2^2)^2 ] ] ] The stabilizer of this partial spread in PGL(4,4) has size 4 and is generated by the images of the matrices: [ [ Z(2^2)^2, 0, 0, 0 ], [ 0, Z(2^2)^2, 0, 0 ], [ 0, 0, Z(2^2)^2, 0 ], [ 0, 0, 0, Z(2^2)^2 ] ], [ [ 0, 0, 1, Z(2^2)^2 ], [ 0, 0, 1, 1 ], [ Z(2^2)^2, Z(2^2), 0, 0 ], [ Z(2^2)^2, Z(2^2)^2, 0, 0 ] ], [ [ Z(2^2)^2, Z(2^2), 1, Z(2^2) ], [ Z(2^2)^2, Z(2^2)^2, Z(2^2), Z(2^2) ], [ 1, 1, Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2)^2 ] ], THE 13 INEQUIVALENT MAXIMAL PARTIAL SPREAD(S) OF SIZE 13: Maximal partial spread: [ [ [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ], [ 0, 0, 1, 1 ], [ 0, 0, 1, Z(2^2) ], [ 0, 0, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 1, 1, 0, 0 ], [ 1, Z(2^2), 0, 0 ], [ 1, Z(2^2)^2, 0, 0 ] ], [ [ 0, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 1, 1, 1, 1 ], [ 1, Z(2^2), 1, Z(2^2) ], [ 1, Z(2^2)^2, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, Z(2^2) ], [ 1, 0, Z(2^2), 0 ], [ 1, 1, Z(2^2), Z(2^2) ], [ 1, Z(2^2), Z(2^2), Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2), 1 ] ], [ [ 0, 1, 0, Z(2^2)^2 ], [ 1, 0, Z(2^2)^2, 0 ], [ 1, 1, Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2), Z(2^2)^2, 1 ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2) ] ], [ [ 0, 1, 1, 0 ], [ 1, 0, 1, Z(2^2) ], [ 1, 1, 0, Z(2^2) ], [ 1, Z(2^2), Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2)^2, Z(2^2), Z(2^2) ] ], [ [ 0, 1, 1, 1 ], [ 1, 0, 0, Z(2^2)^2 ], [ 1, 1, 1, Z(2^2) ], [ 1, Z(2^2), Z(2^2), 1 ], [ 1, Z(2^2)^2, Z(2^2)^2, 0 ] ], [ [ 0, 1, 1, Z(2^2) ], [ 1, 0, Z(2^2)^2, Z(2^2) ], [ 1, 1, Z(2^2), 0 ], [ 1, Z(2^2), 1, 1 ], [ 1, Z(2^2)^2, 0, Z(2^2)^2 ] ], [ [ 0, 1, 1, Z(2^2)^2 ], [ 1, 0, Z(2^2), Z(2^2)^2 ], [ 1, 1, Z(2^2)^2, 0 ], [ 1, Z(2^2), 0, Z(2^2) ], [ 1, Z(2^2)^2, 1, 1 ] ], [ [ 0, 1, Z(2^2), 0 ], [ 1, 0, Z(2^2)^2, Z(2^2)^2 ], [ 1, 1, 1, Z(2^2)^2 ], [ 1, Z(2^2), 0, Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2), Z(2^2)^2 ] ], [ [ 0, 1, Z(2^2), 1 ], [ 1, 0, Z(2^2), Z(2^2) ], [ 1, 1, 0, Z(2^2)^2 ], [ 1, Z(2^2), 1, 0 ], [ 1, Z(2^2)^2, Z(2^2)^2, 1 ] ], [ [ 0, 1, Z(2^2)^2, 1 ], [ 1, 0, Z(2^2), 1 ], [ 1, 1, 1, 0 ], [ 1, Z(2^2), Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2)^2, 0, Z(2^2) ] ], [ [ 0, 1, Z(2^2)^2, Z(2^2)^2 ], [ 1, 0, 0, Z(2^2) ], [ 1, 1, Z(2^2)^2, 1 ], [ 1, Z(2^2), 1, Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2), 0 ] ] ] The stabilizer of this partial spread in PGL(4,4) has size 12 and is generated by the images of the matrices: [ [ Z(2^2)^2, 0, 0, 0 ], [ 0, Z(2^2)^2, 0, 0 ], [ 0, 0, Z(2^2)^2, 0 ], [ 0, 0, 0, Z(2^2)^2 ] ], [ [ 1, 1, Z(2^2)^2, Z(2^2)^2 ], [ 0, 1, 0, Z(2^2)^2 ], [ 0, 0, 1, 1 ], [ 0, 0, 0, 1 ] ], [ [ Z(2^2)^2, Z(2^2), 0, 0 ], [ 0, Z(2^2)^2, 0, 0 ], [ 0, 0, Z(2^2)^2, Z(2^2) ], [ 0, 0, 0, Z(2^2)^2 ] ], [ [ 0, Z(2^2), Z(2^2), 0 ], [ Z(2^2)^2, 1, Z(2^2), 1 ], [ 1, Z(2^2)^2, 0, Z(2^2) ], [ 0, 1, Z(2^2)^2, 1 ] ], Maximal partial spread: [ [ [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ], [ 0, 0, 1, 1 ], [ 0, 0, 1, Z(2^2) ], [ 0, 0, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 1, 1, 0, 0 ], [ 1, Z(2^2), 0, 0 ], [ 1, Z(2^2)^2, 0, 0 ] ], [ [ 0, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 1, 1, 1, 1 ], [ 1, Z(2^2), 1, Z(2^2) ], [ 1, Z(2^2)^2, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, Z(2^2) ], [ 1, 0, Z(2^2), 0 ], [ 1, 1, Z(2^2), Z(2^2) ], [ 1, Z(2^2), Z(2^2), Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2), 1 ] ], [ [ 0, 1, 0, Z(2^2)^2 ], [ 1, 0, Z(2^2)^2, 0 ], [ 1, 1, Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2), Z(2^2)^2, 1 ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2) ] ], [ [ 0, 1, 1, 0 ], [ 1, 0, 1, Z(2^2) ], [ 1, 1, 0, Z(2^2) ], [ 1, Z(2^2), Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2)^2, Z(2^2), Z(2^2) ] ], [ [ 0, 1, 1, 1 ], [ 1, 0, 0, Z(2^2)^2 ], [ 1, 1, 1, Z(2^2) ], [ 1, Z(2^2), Z(2^2), 1 ], [ 1, Z(2^2)^2, Z(2^2)^2, 0 ] ], [ [ 0, 1, 1, Z(2^2) ], [ 1, 0, Z(2^2)^2, Z(2^2) ], [ 1, 1, Z(2^2), 0 ], [ 1, Z(2^2), 1, 1 ], [ 1, Z(2^2)^2, 0, Z(2^2)^2 ] ], [ [ 0, 1, 1, Z(2^2)^2 ], [ 1, 0, Z(2^2), Z(2^2)^2 ], [ 1, 1, Z(2^2)^2, 0 ], [ 1, Z(2^2), 0, Z(2^2) ], [ 1, Z(2^2)^2, 1, 1 ] ], [ [ 0, 1, Z(2^2)^2, 0 ], [ 1, 0, 1, 1 ], [ 1, 1, Z(2^2), 1 ], [ 1, Z(2^2), 0, 1 ], [ 1, Z(2^2)^2, Z(2^2)^2, 1 ] ], [ [ 0, 1, Z(2^2)^2, 1 ], [ 1, 0, Z(2^2), 1 ], [ 1, 1, 1, 0 ], [ 1, Z(2^2), Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2)^2, 0, Z(2^2) ] ], [ [ 0, 1, Z(2^2)^2, Z(2^2) ], [ 1, 0, Z(2^2)^2, 1 ], [ 1, 1, 0, Z(2^2)^2 ], [ 1, Z(2^2), Z(2^2), Z(2^2) ], [ 1, Z(2^2)^2, 1, 0 ] ], [ [ 0, 1, Z(2^2)^2, Z(2^2)^2 ], [ 1, 0, 0, 1 ], [ 1, 1, Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2), 1, 0 ], [ 1, Z(2^2)^2, Z(2^2), Z(2^2)^2 ] ] ] The stabilizer of this partial spread in PGL(4,4) has size 12 and is generated by the images of the matrices: [ [ Z(2^2)^2, 0, 0, 0 ], [ 0, Z(2^2)^2, 0, 0 ], [ 0, 0, Z(2^2)^2, 0 ], [ 0, 0, 0, Z(2^2)^2 ] ], [ [ 1, Z(2^2), Z(2^2)^2, 1 ], [ Z(2^2), 1, 1, Z(2^2)^2 ], [ 0, 0, 1, Z(2^2) ], [ 0, 0, Z(2^2), 1 ] ], [ [ Z(2^2)^2, 1, Z(2^2)^2, 1 ], [ 1, Z(2^2)^2, 1, Z(2^2)^2 ], [ 0, 0, Z(2^2)^2, 1 ], [ 0, 0, 1, Z(2^2)^2 ] ], [ [ Z(2^2), 1, Z(2^2)^2, Z(2^2) ], [ Z(2^2), Z(2^2), Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2), Z(2^2)^2, Z(2^2)^2 ], [ Z(2^2), 1, 0, Z(2^2)^2 ] ], Maximal partial spread: [ [ [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ], [ 0, 0, 1, 1 ], [ 0, 0, 1, Z(2^2) ], [ 0, 0, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 1, 1, 0, 0 ], [ 1, Z(2^2), 0, 0 ], [ 1, Z(2^2)^2, 0, 0 ] ], [ [ 0, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 1, 1, 1, 1 ], [ 1, Z(2^2), 1, Z(2^2) ], [ 1, Z(2^2)^2, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, Z(2^2) ], [ 1, 0, Z(2^2), 0 ], [ 1, 1, Z(2^2), Z(2^2) ], [ 1, Z(2^2), Z(2^2), Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2), 1 ] ], [ [ 0, 1, 0, Z(2^2)^2 ], [ 1, 0, Z(2^2)^2, 0 ], [ 1, 1, Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2), Z(2^2)^2, 1 ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2) ] ], [ [ 0, 1, 1, 0 ], [ 1, 0, 1, Z(2^2) ], [ 1, 1, 0, Z(2^2) ], [ 1, Z(2^2), Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2)^2, Z(2^2), Z(2^2) ] ], [ [ 0, 1, 1, 1 ], [ 1, 0, 0, Z(2^2)^2 ], [ 1, 1, 1, Z(2^2) ], [ 1, Z(2^2), Z(2^2), 1 ], [ 1, Z(2^2)^2, Z(2^2)^2, 0 ] ], [ [ 0, 1, 1, Z(2^2) ], [ 1, 0, Z(2^2)^2, Z(2^2) ], [ 1, 1, Z(2^2), 0 ], [ 1, Z(2^2), 1, 1 ], [ 1, Z(2^2)^2, 0, Z(2^2)^2 ] ], [ [ 0, 1, 1, Z(2^2)^2 ], [ 1, 0, Z(2^2), Z(2^2)^2 ], [ 1, 1, Z(2^2)^2, 0 ], [ 1, Z(2^2), 0, Z(2^2) ], [ 1, Z(2^2)^2, 1, 1 ] ], [ [ 0, 1, Z(2^2)^2, 0 ], [ 1, 0, 1, 1 ], [ 1, 1, Z(2^2), 1 ], [ 1, Z(2^2), 0, 1 ], [ 1, Z(2^2)^2, Z(2^2)^2, 1 ] ], [ [ 0, 1, Z(2^2)^2, 1 ], [ 1, 0, Z(2^2), 1 ], [ 1, 1, 1, 0 ], [ 1, Z(2^2), Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2)^2, 0, Z(2^2) ] ], [ [ 0, 1, Z(2^2)^2, Z(2^2) ], [ 1, 0, Z(2^2)^2, Z(2^2)^2 ], [ 1, 1, 0, 1 ], [ 1, Z(2^2), Z(2^2), 0 ], [ 1, Z(2^2)^2, 1, Z(2^2) ] ], [ [ 0, 1, Z(2^2)^2, Z(2^2)^2 ], [ 1, 0, 0, 1 ], [ 1, 1, Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2), 1, 0 ], [ 1, Z(2^2)^2, Z(2^2), Z(2^2)^2 ] ] ] The stabilizer of this partial spread in PGL(4,4) has size 6 and is generated by the images of the matrices: [ [ Z(2^2)^2, 0, 0, 0 ], [ 0, Z(2^2)^2, 0, 0 ], [ 0, 0, Z(2^2)^2, 0 ], [ 0, 0, 0, Z(2^2)^2 ] ], [ [ Z(2^2), Z(2^2), Z(2^2), Z(2^2) ], [ 0, Z(2^2), 0, Z(2^2) ], [ 0, 0, Z(2^2), Z(2^2) ], [ 0, 0, 0, Z(2^2) ] ], [ [ 0, Z(2^2)^2, 0, Z(2^2)^2 ], [ Z(2^2), Z(2^2), Z(2^2), Z(2^2) ], [ Z(2^2)^2, 0, 1, Z(2^2)^2 ], [ 0, Z(2^2)^2, Z(2^2), Z(2^2)^2 ] ], Maximal partial spread: [ [ [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ], [ 0, 0, 1, 1 ], [ 0, 0, 1, Z(2^2) ], [ 0, 0, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 1, 1, 0, 0 ], [ 1, Z(2^2), 0, 0 ], [ 1, Z(2^2)^2, 0, 0 ] ], [ [ 0, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 1, 1, 1, 1 ], [ 1, Z(2^2), 1, Z(2^2) ], [ 1, Z(2^2)^2, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, Z(2^2) ], [ 1, 0, Z(2^2), 0 ], [ 1, 1, Z(2^2), Z(2^2) ], [ 1, Z(2^2), Z(2^2), Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2), 1 ] ], [ [ 0, 1, 0, Z(2^2)^2 ], [ 1, 0, Z(2^2)^2, 0 ], [ 1, 1, Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2), Z(2^2)^2, 1 ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2) ] ], [ [ 0, 1, 1, 0 ], [ 1, 0, 1, Z(2^2) ], [ 1, 1, 0, Z(2^2) ], [ 1, Z(2^2), Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2)^2, Z(2^2), Z(2^2) ] ], [ [ 0, 1, 1, 1 ], [ 1, 0, 0, Z(2^2)^2 ], [ 1, 1, 1, Z(2^2) ], [ 1, Z(2^2), Z(2^2), 1 ], [ 1, Z(2^2)^2, Z(2^2)^2, 0 ] ], [ [ 0, 1, 1, Z(2^2) ], [ 1, 0, Z(2^2)^2, Z(2^2)^2 ], [ 1, 1, Z(2^2), 1 ], [ 1, Z(2^2), 1, 0 ], [ 1, Z(2^2)^2, 0, Z(2^2) ] ], [ [ 0, 1, 1, Z(2^2)^2 ], [ 1, 0, Z(2^2), Z(2^2) ], [ 1, 1, Z(2^2)^2, 1 ], [ 1, Z(2^2), 0, Z(2^2)^2 ], [ 1, Z(2^2)^2, 1, 0 ] ], [ [ 0, 1, Z(2^2), 0 ], [ 1, 0, Z(2^2), Z(2^2)^2 ], [ 1, 1, 0, Z(2^2)^2 ], [ 1, Z(2^2), 1, Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2)^2 ] ], [ [ 0, 1, Z(2^2), 1 ], [ 1, 0, 0, 1 ], [ 1, 1, Z(2^2), 0 ], [ 1, Z(2^2), Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2)^2, 1, Z(2^2) ] ], [ [ 0, 1, Z(2^2), Z(2^2) ], [ 1, 0, Z(2^2)^2, 1 ], [ 1, 1, 1, Z(2^2)^2 ], [ 1, Z(2^2), 0, Z(2^2) ], [ 1, Z(2^2)^2, Z(2^2), 0 ] ], [ [ 0, 1, Z(2^2), Z(2^2)^2 ], [ 1, 0, 1, Z(2^2)^2 ], [ 1, 1, Z(2^2)^2, 0 ], [ 1, Z(2^2), Z(2^2), Z(2^2) ], [ 1, Z(2^2)^2, 0, 1 ] ] ] The stabilizer of this partial spread in PGL(4,4) has size 12 and is generated by the images of the matrices: [ [ Z(2^2)^2, 0, 0, 0 ], [ 0, Z(2^2)^2, 0, 0 ], [ 0, 0, Z(2^2)^2, 0 ], [ 0, 0, 0, Z(2^2)^2 ] ], [ [ 1, Z(2^2)^2, Z(2^2), 1 ], [ 1, 1, Z(2^2), Z(2^2) ], [ 0, 0, 1, Z(2^2)^2 ], [ 0, 0, 1, 1 ] ], [ [ 1, Z(2^2)^2, 1, Z(2^2)^2 ], [ 1, 1, 1, 1 ], [ 0, 0, 1, Z(2^2)^2 ], [ 0, 0, 1, 1 ] ], [ [ Z(2^2)^2, 0, Z(2^2), 0 ], [ Z(2^2), Z(2^2)^2, 1, Z(2^2) ], [ Z(2^2), 1, 1, 1 ], [ Z(2^2), Z(2^2), 0, 1 ] ], Maximal partial spread: [ [ [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ], [ 0, 0, 1, 1 ], [ 0, 0, 1, Z(2^2) ], [ 0, 0, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 1, 1, 0, 0 ], [ 1, Z(2^2), 0, 0 ], [ 1, Z(2^2)^2, 0, 0 ] ], [ [ 0, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 1, 1, 1, 1 ], [ 1, Z(2^2), 1, Z(2^2) ], [ 1, Z(2^2)^2, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, Z(2^2) ], [ 1, 0, Z(2^2), 0 ], [ 1, 1, Z(2^2), Z(2^2) ], [ 1, Z(2^2), Z(2^2), Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2), 1 ] ], [ [ 0, 1, 0, Z(2^2)^2 ], [ 1, 0, Z(2^2)^2, 0 ], [ 1, 1, Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2), Z(2^2)^2, 1 ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2) ] ], [ [ 0, 1, 1, 0 ], [ 1, 0, 1, Z(2^2) ], [ 1, 1, 0, Z(2^2) ], [ 1, Z(2^2), Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2)^2, Z(2^2), Z(2^2) ] ], [ [ 0, 1, 1, 1 ], [ 1, 0, 0, Z(2^2)^2 ], [ 1, 1, 1, Z(2^2) ], [ 1, Z(2^2), Z(2^2), 1 ], [ 1, Z(2^2)^2, Z(2^2)^2, 0 ] ], [ [ 0, 1, 1, Z(2^2) ], [ 1, 0, Z(2^2)^2, Z(2^2)^2 ], [ 1, 1, Z(2^2), 1 ], [ 1, Z(2^2), 1, 0 ], [ 1, Z(2^2)^2, 0, Z(2^2) ] ], [ [ 0, 1, 1, Z(2^2)^2 ], [ 1, 0, Z(2^2), Z(2^2) ], [ 1, 1, Z(2^2)^2, 1 ], [ 1, Z(2^2), 0, Z(2^2)^2 ], [ 1, Z(2^2)^2, 1, 0 ] ], [ [ 0, 1, Z(2^2), 0 ], [ 1, 0, Z(2^2), Z(2^2)^2 ], [ 1, 1, 0, Z(2^2)^2 ], [ 1, Z(2^2), 1, Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2)^2 ] ], [ [ 0, 1, Z(2^2), 1 ], [ 1, 0, 0, 1 ], [ 1, 1, Z(2^2), 0 ], [ 1, Z(2^2), Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2)^2, 1, Z(2^2) ] ], [ [ 0, 1, Z(2^2), Z(2^2) ], [ 1, 0, Z(2^2)^2, Z(2^2) ], [ 1, 1, 1, 0 ], [ 1, Z(2^2), 0, 1 ], [ 1, Z(2^2)^2, Z(2^2), Z(2^2)^2 ] ], [ [ 0, 1, Z(2^2), Z(2^2)^2 ], [ 1, 0, 1, Z(2^2)^2 ], [ 1, 1, Z(2^2)^2, 0 ], [ 1, Z(2^2), Z(2^2), Z(2^2) ], [ 1, Z(2^2)^2, 0, 1 ] ] ] The stabilizer of this partial spread in PGL(4,4) has size 6 and is generated by the images of the matrices: [ [ Z(2^2)^2, 0, 0, 0 ], [ 0, Z(2^2)^2, 0, 0 ], [ 0, 0, Z(2^2)^2, 0 ], [ 0, 0, 0, Z(2^2)^2 ] ], [ [ Z(2^2), Z(2^2), Z(2^2), Z(2^2) ], [ 0, Z(2^2), 0, Z(2^2) ], [ 0, 0, Z(2^2), Z(2^2) ], [ 0, 0, 0, Z(2^2) ] ], [ [ Z(2^2)^2, Z(2^2), Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2), 1, Z(2^2) ], [ Z(2^2)^2, 0, 1, Z(2^2) ], [ 0, Z(2^2)^2, 1, 0 ] ], Maximal partial spread: [ [ [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ], [ 0, 0, 1, 1 ], [ 0, 0, 1, Z(2^2) ], [ 0, 0, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 1, 1, 0, 0 ], [ 1, Z(2^2), 0, 0 ], [ 1, Z(2^2)^2, 0, 0 ] ], [ [ 0, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 1, 1, 1, 1 ], [ 1, Z(2^2), 1, Z(2^2) ], [ 1, Z(2^2)^2, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, Z(2^2) ], [ 1, 0, Z(2^2), 0 ], [ 1, 1, Z(2^2), Z(2^2) ], [ 1, Z(2^2), Z(2^2), Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2), 1 ] ], [ [ 0, 1, 0, Z(2^2)^2 ], [ 1, 0, Z(2^2)^2, 0 ], [ 1, 1, Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2), Z(2^2)^2, 1 ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2) ] ], [ [ 0, 1, 1, 0 ], [ 1, 0, 1, Z(2^2) ], [ 1, 1, 0, Z(2^2) ], [ 1, Z(2^2), Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2)^2, Z(2^2), Z(2^2) ] ], [ [ 0, 1, 1, 1 ], [ 1, 0, Z(2^2), 1 ], [ 1, 1, Z(2^2)^2, 0 ], [ 1, Z(2^2), 0, Z(2^2)^2 ], [ 1, Z(2^2)^2, 1, Z(2^2) ] ], [ [ 0, 1, 1, Z(2^2) ], [ 1, 0, Z(2^2)^2, Z(2^2) ], [ 1, 1, Z(2^2), 0 ], [ 1, Z(2^2), 1, 1 ], [ 1, Z(2^2)^2, 0, Z(2^2)^2 ] ], [ [ 0, 1, 1, Z(2^2)^2 ], [ 1, 0, 0, 1 ], [ 1, 1, 1, Z(2^2) ], [ 1, Z(2^2), Z(2^2), 0 ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2)^2 ] ], [ [ 0, 1, Z(2^2), 0 ], [ 1, 0, 1, 1 ], [ 1, 1, Z(2^2)^2, 1 ], [ 1, Z(2^2), Z(2^2), 1 ], [ 1, Z(2^2)^2, 0, 1 ] ], [ [ 0, 1, Z(2^2), 1 ], [ 1, 0, Z(2^2), Z(2^2) ], [ 1, 1, 0, Z(2^2)^2 ], [ 1, Z(2^2), 1, 0 ], [ 1, Z(2^2)^2, Z(2^2)^2, 1 ] ], [ [ 0, 1, Z(2^2), Z(2^2) ], [ 1, 0, Z(2^2)^2, 1 ], [ 1, 1, 1, Z(2^2)^2 ], [ 1, Z(2^2), 0, Z(2^2) ], [ 1, Z(2^2)^2, Z(2^2), 0 ] ], [ [ 0, 1, Z(2^2), Z(2^2)^2 ], [ 1, 0, 0, Z(2^2) ], [ 1, 1, Z(2^2), 1 ], [ 1, Z(2^2), Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2)^2, 1, 0 ] ] ] The stabilizer of this partial spread in PGL(4,4) has size 8 and is generated by the images of the matrices: [ [ Z(2^2)^2, 0, 0, 0 ], [ 0, Z(2^2)^2, 0, 0 ], [ 0, 0, Z(2^2)^2, 0 ], [ 0, 0, 0, Z(2^2)^2 ] ], [ [ 0, Z(2^2), 0, 1 ], [ Z(2^2), 0, 1, 0 ], [ 0, 0, 0, Z(2^2) ], [ 0, 0, Z(2^2), 0 ] ], [ [ Z(2^2)^2, Z(2^2), 0, 0 ], [ Z(2^2), Z(2^2)^2, 0, 0 ], [ 0, 0, Z(2^2)^2, Z(2^2) ], [ 0, 0, Z(2^2), Z(2^2)^2 ] ], [ [ Z(2^2), 1, Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2), Z(2^2), Z(2^2)^2 ], [ 0, 0, Z(2^2), 1 ], [ 0, 0, 1, Z(2^2) ] ], Maximal partial spread: [ [ [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ], [ 0, 0, 1, 1 ], [ 0, 0, 1, Z(2^2) ], [ 0, 0, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 1, 1, 0, 0 ], [ 1, Z(2^2), 0, 0 ], [ 1, Z(2^2)^2, 0, 0 ] ], [ [ 0, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 1, 1, 1, 1 ], [ 1, Z(2^2), 1, Z(2^2) ], [ 1, Z(2^2)^2, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, Z(2^2) ], [ 1, 0, Z(2^2), 0 ], [ 1, 1, Z(2^2), Z(2^2) ], [ 1, Z(2^2), Z(2^2), Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2), 1 ] ], [ [ 0, 1, 0, Z(2^2)^2 ], [ 1, 0, Z(2^2)^2, 0 ], [ 1, 1, Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2), Z(2^2)^2, 1 ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2) ] ], [ [ 0, 1, 1, 0 ], [ 1, 0, 1, Z(2^2) ], [ 1, 1, 0, Z(2^2) ], [ 1, Z(2^2), Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2)^2, Z(2^2), Z(2^2) ] ], [ [ 0, 1, 1, 1 ], [ 1, 0, Z(2^2), 1 ], [ 1, 1, Z(2^2)^2, 0 ], [ 1, Z(2^2), 0, Z(2^2)^2 ], [ 1, Z(2^2)^2, 1, Z(2^2) ] ], [ [ 0, 1, 1, Z(2^2) ], [ 1, 0, Z(2^2)^2, Z(2^2)^2 ], [ 1, 1, Z(2^2), 1 ], [ 1, Z(2^2), 1, 0 ], [ 1, Z(2^2)^2, 0, Z(2^2) ] ], [ [ 0, 1, 1, Z(2^2)^2 ], [ 1, 0, 0, 1 ], [ 1, 1, 1, Z(2^2) ], [ 1, Z(2^2), Z(2^2), 0 ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2)^2 ] ], [ [ 0, 1, Z(2^2), Z(2^2) ], [ 1, 0, Z(2^2)^2, Z(2^2) ], [ 1, 1, 1, 0 ], [ 1, Z(2^2), 0, 1 ], [ 1, Z(2^2)^2, Z(2^2), Z(2^2)^2 ] ], [ [ 0, 1, Z(2^2)^2, 0 ], [ 1, 0, Z(2^2)^2, 1 ], [ 1, 1, 0, 1 ], [ 1, Z(2^2), Z(2^2), 1 ], [ 1, Z(2^2)^2, 1, 1 ] ], [ [ 0, 1, Z(2^2)^2, 1 ], [ 1, 0, 0, Z(2^2)^2 ], [ 1, 1, Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2), 1, 1 ], [ 1, Z(2^2)^2, Z(2^2), 0 ] ], [ [ 0, 1, Z(2^2)^2, Z(2^2) ], [ 1, 0, 1, 1 ], [ 1, 1, Z(2^2), Z(2^2)^2 ], [ 1, Z(2^2), 0, Z(2^2) ], [ 1, Z(2^2)^2, Z(2^2)^2, 0 ] ] ] The stabilizer of this partial spread in PGL(4,4) has size 12 and is generated by the images of the matrices: [ [ Z(2^2)^2, 0, 0, 0 ], [ 0, Z(2^2)^2, 0, 0 ], [ 0, 0, Z(2^2)^2, 0 ], [ 0, 0, 0, Z(2^2)^2 ] ], [ [ Z(2^2)^2, 0, Z(2^2)^2, 0 ], [ 1, Z(2^2)^2, 1, Z(2^2)^2 ], [ 0, 0, Z(2^2)^2, 0 ], [ 0, 0, 1, Z(2^2)^2 ] ], [ [ Z(2^2), 0, 0, 0 ], [ Z(2^2), Z(2^2), 0, 0 ], [ 0, 0, Z(2^2), 0 ], [ 0, 0, Z(2^2), Z(2^2) ] ], [ [ Z(2^2), Z(2^2)^2, 0, Z(2^2)^2 ], [ Z(2^2), 0, Z(2^2), Z(2^2) ], [ Z(2^2), 0, Z(2^2), Z(2^2)^2 ], [ 0, Z(2^2), Z(2^2), 0 ] ], Maximal partial spread: [ [ [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ], [ 0, 0, 1, 1 ], [ 0, 0, 1, Z(2^2) ], [ 0, 0, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 1, 1, 0, 0 ], [ 1, Z(2^2), 0, 0 ], [ 1, Z(2^2)^2, 0, 0 ] ], [ [ 0, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 1, 1, 1, 1 ], [ 1, Z(2^2), 1, Z(2^2) ], [ 1, Z(2^2)^2, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, Z(2^2) ], [ 1, 0, Z(2^2), 0 ], [ 1, 1, Z(2^2), Z(2^2) ], [ 1, Z(2^2), Z(2^2), Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2), 1 ] ], [ [ 0, 1, 0, Z(2^2)^2 ], [ 1, 0, Z(2^2)^2, 1 ], [ 1, 1, Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2), Z(2^2)^2, 0 ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2)^2 ] ], [ [ 0, 1, 1, 0 ], [ 1, 0, 0, Z(2^2) ], [ 1, 1, 1, Z(2^2) ], [ 1, Z(2^2), Z(2^2), Z(2^2) ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2) ] ], [ [ 0, 1, 1, 1 ], [ 1, 0, 1, Z(2^2)^2 ], [ 1, 1, 0, Z(2^2) ], [ 1, Z(2^2), Z(2^2)^2, 1 ], [ 1, Z(2^2)^2, Z(2^2), 0 ] ], [ [ 0, 1, 1, Z(2^2) ], [ 1, 0, Z(2^2), 1 ], [ 1, 1, Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2), 0, Z(2^2) ], [ 1, Z(2^2)^2, 1, 0 ] ], [ [ 0, 1, 1, Z(2^2)^2 ], [ 1, 0, Z(2^2)^2, 0 ], [ 1, 1, Z(2^2), Z(2^2)^2 ], [ 1, Z(2^2), 1, 1 ], [ 1, Z(2^2)^2, 0, Z(2^2) ] ], [ [ 0, 1, Z(2^2), 0 ], [ 1, 0, 1, 1 ], [ 1, 1, Z(2^2)^2, 1 ], [ 1, Z(2^2), Z(2^2), 1 ], [ 1, Z(2^2)^2, 0, 1 ] ], [ [ 0, 1, Z(2^2), 1 ], [ 1, 0, 0, 1 ], [ 1, 1, Z(2^2), 0 ], [ 1, Z(2^2), Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2)^2, 1, Z(2^2) ] ], [ [ 0, 1, Z(2^2), Z(2^2) ], [ 1, 0, Z(2^2)^2, Z(2^2) ], [ 1, 1, 1, 0 ], [ 1, Z(2^2), 0, 1 ], [ 1, Z(2^2)^2, Z(2^2), Z(2^2)^2 ] ], [ [ 0, 1, Z(2^2), Z(2^2)^2 ], [ 1, 0, Z(2^2), Z(2^2) ], [ 1, 1, 0, 1 ], [ 1, Z(2^2), 1, Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2)^2, 0 ] ] ] The stabilizer of this partial spread in PGL(4,4) has size 8 and is generated by the images of the matrices: [ [ Z(2^2)^2, 0, 0, 0 ], [ 0, Z(2^2)^2, 0, 0 ], [ 0, 0, Z(2^2)^2, 0 ], [ 0, 0, 0, Z(2^2)^2 ] ], [ [ Z(2^2), Z(2^2)^2, 0, 0 ], [ 0, Z(2^2), 0, 0 ], [ 0, 0, Z(2^2), Z(2^2)^2 ], [ 0, 0, 0, Z(2^2) ] ], [ [ Z(2^2), Z(2^2), 0, 0 ], [ 0, Z(2^2), 0, 0 ], [ 0, 0, Z(2^2), Z(2^2) ], [ 0, 0, 0, Z(2^2) ] ], [ [ 0, 0, Z(2^2)^2, Z(2^2)^2 ], [ 0, 0, 0, Z(2^2)^2 ], [ Z(2^2), Z(2^2), 0, 0 ], [ 0, Z(2^2), 0, 0 ] ], Maximal partial spread: [ [ [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ], [ 0, 0, 1, 1 ], [ 0, 0, 1, Z(2^2) ], [ 0, 0, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 1, 1, 0, 0 ], [ 1, Z(2^2), 0, 0 ], [ 1, Z(2^2)^2, 0, 0 ] ], [ [ 0, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 1, 1, 1, 1 ], [ 1, Z(2^2), 1, Z(2^2) ], [ 1, Z(2^2)^2, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, Z(2^2) ], [ 1, 0, Z(2^2), 0 ], [ 1, 1, Z(2^2), Z(2^2) ], [ 1, Z(2^2), Z(2^2), Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2), 1 ] ], [ [ 0, 1, 0, Z(2^2)^2 ], [ 1, 0, Z(2^2)^2, 1 ], [ 1, 1, Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2), Z(2^2)^2, 0 ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2)^2 ] ], [ [ 0, 1, 1, 0 ], [ 1, 0, 0, Z(2^2) ], [ 1, 1, 1, Z(2^2) ], [ 1, Z(2^2), Z(2^2), Z(2^2) ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2) ] ], [ [ 0, 1, 1, 1 ], [ 1, 0, 1, Z(2^2)^2 ], [ 1, 1, 0, Z(2^2) ], [ 1, Z(2^2), Z(2^2)^2, 1 ], [ 1, Z(2^2)^2, Z(2^2), 0 ] ], [ [ 0, 1, 1, Z(2^2) ], [ 1, 0, Z(2^2), 1 ], [ 1, 1, Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2), 0, Z(2^2) ], [ 1, Z(2^2)^2, 1, 0 ] ], [ [ 0, 1, 1, Z(2^2)^2 ], [ 1, 0, Z(2^2)^2, 0 ], [ 1, 1, Z(2^2), Z(2^2)^2 ], [ 1, Z(2^2), 1, 1 ], [ 1, Z(2^2)^2, 0, Z(2^2) ] ], [ [ 0, 1, Z(2^2), 0 ], [ 1, 0, 1, 1 ], [ 1, 1, Z(2^2)^2, 1 ], [ 1, Z(2^2), Z(2^2), 1 ], [ 1, Z(2^2)^2, 0, 1 ] ], [ [ 0, 1, Z(2^2), 1 ], [ 1, 0, 0, 1 ], [ 1, 1, Z(2^2), 0 ], [ 1, Z(2^2), Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2)^2, 1, Z(2^2) ] ], [ [ 0, 1, Z(2^2), Z(2^2) ], [ 1, 0, Z(2^2)^2, Z(2^2) ], [ 1, 1, 1, 0 ], [ 1, Z(2^2), 0, 1 ], [ 1, Z(2^2)^2, Z(2^2), Z(2^2)^2 ] ], [ [ 0, 1, Z(2^2)^2, Z(2^2)^2 ], [ 1, 0, 1, Z(2^2) ], [ 1, 1, Z(2^2), 1 ], [ 1, Z(2^2), 0, Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2)^2, 0 ] ] ] The stabilizer of this partial spread in PGL(4,4) has size 2 and is generated by the images of the matrices: [ [ Z(2^2)^2, 0, 0, 0 ], [ 0, Z(2^2)^2, 0, 0 ], [ 0, 0, Z(2^2)^2, 0 ], [ 0, 0, 0, Z(2^2)^2 ] ], [ [ 0, 0, 1, Z(2^2)^2 ], [ 0, 0, 0, 1 ], [ Z(2^2)^2, Z(2^2), 0, 0 ], [ 0, Z(2^2)^2, 0, 0 ] ], Maximal partial spread: [ [ [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ], [ 0, 0, 1, 1 ], [ 0, 0, 1, Z(2^2) ], [ 0, 0, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 1, 1, 0, 0 ], [ 1, Z(2^2), 0, 0 ], [ 1, Z(2^2)^2, 0, 0 ] ], [ [ 0, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 1, 1, 1, 1 ], [ 1, Z(2^2), 1, Z(2^2) ], [ 1, Z(2^2)^2, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, Z(2^2) ], [ 1, 0, Z(2^2), 0 ], [ 1, 1, Z(2^2), Z(2^2) ], [ 1, Z(2^2), Z(2^2), Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2), 1 ] ], [ [ 0, 1, 0, Z(2^2)^2 ], [ 1, 0, Z(2^2)^2, 1 ], [ 1, 1, Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2), Z(2^2)^2, 0 ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2)^2 ] ], [ [ 0, 1, 1, 0 ], [ 1, 0, 0, Z(2^2) ], [ 1, 1, 1, Z(2^2) ], [ 1, Z(2^2), Z(2^2), Z(2^2) ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2) ] ], [ [ 0, 1, 1, 1 ], [ 1, 0, 1, Z(2^2)^2 ], [ 1, 1, 0, Z(2^2) ], [ 1, Z(2^2), Z(2^2)^2, 1 ], [ 1, Z(2^2)^2, Z(2^2), 0 ] ], [ [ 0, 1, 1, Z(2^2) ], [ 1, 0, Z(2^2), 1 ], [ 1, 1, Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2), 0, Z(2^2) ], [ 1, Z(2^2)^2, 1, 0 ] ], [ [ 0, 1, 1, Z(2^2)^2 ], [ 1, 0, Z(2^2)^2, 0 ], [ 1, 1, Z(2^2), Z(2^2)^2 ], [ 1, Z(2^2), 1, 1 ], [ 1, Z(2^2)^2, 0, Z(2^2) ] ], [ [ 0, 1, Z(2^2), 0 ], [ 1, 0, 1, 1 ], [ 1, 1, Z(2^2)^2, 1 ], [ 1, Z(2^2), Z(2^2), 1 ], [ 1, Z(2^2)^2, 0, 1 ] ], [ [ 0, 1, Z(2^2), 1 ], [ 1, 0, 0, 1 ], [ 1, 1, Z(2^2), 0 ], [ 1, Z(2^2), Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2)^2, 1, Z(2^2) ] ], [ [ 0, 1, Z(2^2)^2, 1 ], [ 1, 0, Z(2^2)^2, Z(2^2) ], [ 1, 1, 0, Z(2^2)^2 ], [ 1, Z(2^2), Z(2^2), 0 ], [ 1, Z(2^2)^2, 1, 1 ] ], [ [ 0, 1, Z(2^2)^2, Z(2^2)^2 ], [ 1, 0, 1, Z(2^2) ], [ 1, 1, Z(2^2), 1 ], [ 1, Z(2^2), 0, Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2)^2, 0 ] ] ] The stabilizer of this partial spread in PGL(4,4) has size 8 and is generated by the images of the matrices: [ [ Z(2^2)^2, 0, 0, 0 ], [ 0, Z(2^2)^2, 0, 0 ], [ 0, 0, Z(2^2)^2, 0 ], [ 0, 0, 0, Z(2^2)^2 ] ], [ [ Z(2^2)^2, Z(2^2), 0, 0 ], [ 0, Z(2^2)^2, 0, 0 ], [ 0, 0, Z(2^2)^2, Z(2^2) ], [ 0, 0, 0, Z(2^2)^2 ] ], [ [ 0, 0, Z(2^2)^2, 0 ], [ 0, 0, 0, Z(2^2)^2 ], [ Z(2^2), 0, 0, 0 ], [ 0, Z(2^2), 0, 0 ] ], [ [ Z(2^2)^2, Z(2^2), 1, Z(2^2)^2 ], [ 0, Z(2^2)^2, 0, 1 ], [ Z(2^2)^2, Z(2^2), Z(2^2)^2, Z(2^2) ], [ 0, Z(2^2)^2, 0, Z(2^2)^2 ] ], Maximal partial spread: [ [ [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ], [ 0, 0, 1, 1 ], [ 0, 0, 1, Z(2^2) ], [ 0, 0, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 1, 1, 0, 0 ], [ 1, Z(2^2), 0, 0 ], [ 1, Z(2^2)^2, 0, 0 ] ], [ [ 0, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 1, 1, 1, 1 ], [ 1, Z(2^2), 1, Z(2^2) ], [ 1, Z(2^2)^2, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, Z(2^2) ], [ 1, 0, Z(2^2), 0 ], [ 1, 1, Z(2^2), Z(2^2) ], [ 1, Z(2^2), Z(2^2), Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2), 1 ] ], [ [ 0, 1, 0, Z(2^2)^2 ], [ 1, 0, Z(2^2)^2, 1 ], [ 1, 1, Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2), Z(2^2)^2, 0 ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2)^2 ] ], [ [ 0, 1, 1, 0 ], [ 1, 0, 0, Z(2^2) ], [ 1, 1, 1, Z(2^2) ], [ 1, Z(2^2), Z(2^2), Z(2^2) ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2) ] ], [ [ 0, 1, 1, 1 ], [ 1, 0, 1, Z(2^2)^2 ], [ 1, 1, 0, Z(2^2) ], [ 1, Z(2^2), Z(2^2)^2, 1 ], [ 1, Z(2^2)^2, Z(2^2), 0 ] ], [ [ 0, 1, 1, Z(2^2) ], [ 1, 0, Z(2^2), 1 ], [ 1, 1, Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2), 0, Z(2^2) ], [ 1, Z(2^2)^2, 1, 0 ] ], [ [ 0, 1, Z(2^2), 0 ], [ 1, 0, 1, 1 ], [ 1, 1, Z(2^2)^2, 1 ], [ 1, Z(2^2), Z(2^2), 1 ], [ 1, Z(2^2)^2, 0, 1 ] ], [ [ 0, 1, Z(2^2), 1 ], [ 1, 0, 0, 1 ], [ 1, 1, Z(2^2), 0 ], [ 1, Z(2^2), Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2)^2, 1, Z(2^2) ] ], [ [ 0, 1, Z(2^2), Z(2^2)^2 ], [ 1, 0, Z(2^2)^2, 0 ], [ 1, 1, 1, Z(2^2)^2 ], [ 1, Z(2^2), 0, 1 ], [ 1, Z(2^2)^2, Z(2^2), Z(2^2) ] ], [ [ 0, 1, Z(2^2)^2, 1 ], [ 1, 0, Z(2^2)^2, Z(2^2) ], [ 1, 1, 0, Z(2^2)^2 ], [ 1, Z(2^2), Z(2^2), 0 ], [ 1, Z(2^2)^2, 1, 1 ] ], [ [ 0, 1, Z(2^2)^2, Z(2^2)^2 ], [ 1, 0, 1, Z(2^2) ], [ 1, 1, Z(2^2), 1 ], [ 1, Z(2^2), 0, Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2)^2, 0 ] ] ] The stabilizer of this partial spread in PGL(4,4) has size 8 and is generated by the images of the matrices: [ [ Z(2^2)^2, 0, 0, 0 ], [ 0, Z(2^2)^2, 0, 0 ], [ 0, 0, Z(2^2)^2, 0 ], [ 0, 0, 0, Z(2^2)^2 ] ], [ [ Z(2^2)^2, Z(2^2)^2, 0, 0 ], [ Z(2^2), Z(2^2)^2, 0, 0 ], [ 0, 0, Z(2^2)^2, Z(2^2)^2 ], [ 0, 0, Z(2^2), Z(2^2)^2 ] ], [ [ 0, 0, Z(2^2)^2, 0 ], [ 0, 0, 0, Z(2^2)^2 ], [ Z(2^2), 0, 0, 0 ], [ 0, Z(2^2), 0, 0 ] ], [ [ Z(2^2), Z(2^2), Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2), Z(2^2), Z(2^2)^2 ], [ Z(2^2), Z(2^2), Z(2^2), Z(2^2) ], [ 1, Z(2^2), 1, Z(2^2) ] ], Maximal partial spread: [ [ [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ], [ 0, 0, 1, 1 ], [ 0, 0, 1, Z(2^2) ], [ 0, 0, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 1, 1, 0, 0 ], [ 1, Z(2^2), 0, 0 ], [ 1, Z(2^2)^2, 0, 0 ] ], [ [ 0, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 1, 1, 1, 1 ], [ 1, Z(2^2), 1, Z(2^2) ], [ 1, Z(2^2)^2, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, Z(2^2) ], [ 1, 0, Z(2^2), 0 ], [ 1, 1, Z(2^2), Z(2^2) ], [ 1, Z(2^2), Z(2^2), Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2), 1 ] ], [ [ 0, 1, 0, Z(2^2)^2 ], [ 1, 0, Z(2^2)^2, 1 ], [ 1, 1, Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2), Z(2^2)^2, 0 ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2)^2 ] ], [ [ 0, 1, 1, 0 ], [ 1, 0, 0, Z(2^2) ], [ 1, 1, 1, Z(2^2) ], [ 1, Z(2^2), Z(2^2), Z(2^2) ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2) ] ], [ [ 0, 1, 1, 1 ], [ 1, 0, 1, Z(2^2)^2 ], [ 1, 1, 0, Z(2^2) ], [ 1, Z(2^2), Z(2^2)^2, 1 ], [ 1, Z(2^2)^2, Z(2^2), 0 ] ], [ [ 0, 1, 1, Z(2^2) ], [ 1, 0, Z(2^2), 1 ], [ 1, 1, Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2), 0, Z(2^2) ], [ 1, Z(2^2)^2, 1, 0 ] ], [ [ 0, 1, Z(2^2), 0 ], [ 1, 0, 1, 1 ], [ 1, 1, Z(2^2)^2, 1 ], [ 1, Z(2^2), Z(2^2), 1 ], [ 1, Z(2^2)^2, 0, 1 ] ], [ [ 0, 1, Z(2^2), 1 ], [ 1, 0, Z(2^2), Z(2^2) ], [ 1, 1, 0, Z(2^2)^2 ], [ 1, Z(2^2), 1, 0 ], [ 1, Z(2^2)^2, Z(2^2)^2, 1 ] ], [ [ 0, 1, Z(2^2), Z(2^2)^2 ], [ 1, 0, Z(2^2)^2, 0 ], [ 1, 1, 1, Z(2^2)^2 ], [ 1, Z(2^2), 0, 1 ], [ 1, Z(2^2)^2, Z(2^2), Z(2^2) ] ], [ [ 0, 1, Z(2^2)^2, Z(2^2) ], [ 1, 0, Z(2^2)^2, Z(2^2)^2 ], [ 1, 1, 0, 1 ], [ 1, Z(2^2), Z(2^2), 0 ], [ 1, Z(2^2)^2, 1, Z(2^2) ] ], [ [ 0, 1, Z(2^2)^2, Z(2^2)^2 ], [ 1, 0, 1, Z(2^2) ], [ 1, 1, Z(2^2), 1 ], [ 1, Z(2^2), 0, Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2)^2, 0 ] ] ] The stabilizer of this partial spread in PGL(4,4) has size 12 and is generated by the images of the matrices: [ [ Z(2^2)^2, 0, 0, 0 ], [ 0, Z(2^2)^2, 0, 0 ], [ 0, 0, Z(2^2)^2, 0 ], [ 0, 0, 0, Z(2^2)^2 ] ], [ [ 0, Z(2^2), 1, 1 ], [ Z(2^2)^2, 0, Z(2^2)^2, 1 ], [ 0, 0, 1, Z(2^2)^2 ], [ 0, 0, 0, 1 ] ], [ [ Z(2^2)^2, 0, Z(2^2)^2, 1 ], [ 0, Z(2^2)^2, Z(2^2), Z(2^2) ], [ 1, Z(2^2)^2, 0, 0 ], [ 1, Z(2^2), 0, 0 ] ], [ [ 1, Z(2^2)^2, 0, 1 ], [ 1, Z(2^2), Z(2^2), 1 ], [ 1, Z(2^2)^2, 1, Z(2^2)^2 ], [ 1, Z(2^2), 1, Z(2^2) ] ], Maximal partial spread: [ [ [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ], [ 0, 0, 1, 1 ], [ 0, 0, 1, Z(2^2) ], [ 0, 0, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 1, 1, 0, 0 ], [ 1, Z(2^2), 0, 0 ], [ 1, Z(2^2)^2, 0, 0 ] ], [ [ 0, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 1, 1, 1, 1 ], [ 1, Z(2^2), 1, Z(2^2) ], [ 1, Z(2^2)^2, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, Z(2^2) ], [ 1, 0, Z(2^2), 0 ], [ 1, 1, Z(2^2), Z(2^2) ], [ 1, Z(2^2), Z(2^2), Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2), 1 ] ], [ [ 0, 1, 0, Z(2^2)^2 ], [ 1, 0, Z(2^2)^2, 1 ], [ 1, 1, Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2), Z(2^2)^2, 0 ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2)^2 ] ], [ [ 0, 1, 1, 0 ], [ 1, 0, 0, Z(2^2) ], [ 1, 1, 1, Z(2^2) ], [ 1, Z(2^2), Z(2^2), Z(2^2) ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2) ] ], [ [ 0, 1, 1, 1 ], [ 1, 0, 1, Z(2^2)^2 ], [ 1, 1, 0, Z(2^2) ], [ 1, Z(2^2), Z(2^2)^2, 1 ], [ 1, Z(2^2)^2, Z(2^2), 0 ] ], [ [ 0, 1, 1, Z(2^2) ], [ 1, 0, Z(2^2), 1 ], [ 1, 1, Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2), 0, Z(2^2) ], [ 1, Z(2^2)^2, 1, 0 ] ], [ [ 0, 1, Z(2^2), 0 ], [ 1, 0, Z(2^2)^2, Z(2^2)^2 ], [ 1, 1, 1, Z(2^2)^2 ], [ 1, Z(2^2), 0, Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2), Z(2^2)^2 ] ], [ [ 0, 1, Z(2^2), Z(2^2)^2 ], [ 1, 0, Z(2^2), Z(2^2) ], [ 1, 1, 0, 1 ], [ 1, Z(2^2), 1, Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2)^2, 0 ] ], [ [ 0, 1, Z(2^2)^2, 0 ], [ 1, 0, 1, 1 ], [ 1, 1, Z(2^2), 1 ], [ 1, Z(2^2), 0, 1 ], [ 1, Z(2^2)^2, Z(2^2)^2, 1 ] ], [ [ 0, 1, Z(2^2)^2, Z(2^2) ], [ 1, 0, 0, Z(2^2)^2 ], [ 1, 1, Z(2^2)^2, 1 ], [ 1, Z(2^2), 1, 0 ], [ 1, Z(2^2)^2, Z(2^2), Z(2^2) ] ], [ [ 0, 1, Z(2^2)^2, Z(2^2)^2 ], [ 1, 0, Z(2^2)^2, 0 ], [ 1, 1, 0, Z(2^2)^2 ], [ 1, Z(2^2), Z(2^2), 1 ], [ 1, Z(2^2)^2, 1, Z(2^2) ] ] ] The stabilizer of this partial spread in PGL(4,4) has size 12 and is generated by the images of the matrices: [ [ Z(2^2)^2, 0, 0, 0 ], [ 0, Z(2^2)^2, 0, 0 ], [ 0, 0, Z(2^2)^2, 0 ], [ 0, 0, 0, Z(2^2)^2 ] ], [ [ Z(2^2)^2, 1, 0, 0 ], [ 0, Z(2^2)^2, 0, 0 ], [ 0, 0, 0, Z(2^2) ], [ 0, 0, 1, 0 ] ], [ [ 0, 0, Z(2^2), Z(2^2) ], [ 0, 0, Z(2^2)^2, Z(2^2) ], [ 1, 1, 0, 0 ], [ Z(2^2), 1, 0, 0 ] ], [ [ Z(2^2), Z(2^2), Z(2^2)^2, Z(2^2)^2 ], [ Z(2^2)^2, Z(2^2), 1, Z(2^2)^2 ], [ Z(2^2), Z(2^2), Z(2^2), Z(2^2) ], [ Z(2^2)^2, Z(2^2), Z(2^2)^2, Z(2^2) ] ], THE 4 INEQUIVALENT MAXIMAL PARTIAL SPREAD(S) OF SIZE 14: Maximal partial spread: [ [ [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ], [ 0, 0, 1, 1 ], [ 0, 0, 1, Z(2^2) ], [ 0, 0, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 1, 1, 0, 0 ], [ 1, Z(2^2), 0, 0 ], [ 1, Z(2^2)^2, 0, 0 ] ], [ [ 0, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 1, 1, 1, 1 ], [ 1, Z(2^2), 1, Z(2^2) ], [ 1, Z(2^2)^2, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, Z(2^2) ], [ 1, 0, Z(2^2), 0 ], [ 1, 1, Z(2^2), Z(2^2) ], [ 1, Z(2^2), Z(2^2), Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2), 1 ] ], [ [ 0, 1, 0, Z(2^2)^2 ], [ 1, 0, Z(2^2)^2, 0 ], [ 1, 1, Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2), Z(2^2)^2, 1 ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2) ] ], [ [ 0, 1, 1, 0 ], [ 1, 0, 1, Z(2^2) ], [ 1, 1, 0, Z(2^2) ], [ 1, Z(2^2), Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2)^2, Z(2^2), Z(2^2) ] ], [ [ 0, 1, 1, 1 ], [ 1, 0, 0, Z(2^2)^2 ], [ 1, 1, 1, Z(2^2) ], [ 1, Z(2^2), Z(2^2), 1 ], [ 1, Z(2^2)^2, Z(2^2)^2, 0 ] ], [ [ 0, 1, 1, Z(2^2) ], [ 1, 0, Z(2^2)^2, Z(2^2) ], [ 1, 1, Z(2^2), 0 ], [ 1, Z(2^2), 1, 1 ], [ 1, Z(2^2)^2, 0, Z(2^2)^2 ] ], [ [ 0, 1, 1, Z(2^2)^2 ], [ 1, 0, Z(2^2), Z(2^2)^2 ], [ 1, 1, Z(2^2)^2, 0 ], [ 1, Z(2^2), 0, Z(2^2) ], [ 1, Z(2^2)^2, 1, 1 ] ], [ [ 0, 1, Z(2^2), 0 ], [ 1, 0, Z(2^2)^2, Z(2^2)^2 ], [ 1, 1, 1, Z(2^2)^2 ], [ 1, Z(2^2), 0, Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2), Z(2^2)^2 ] ], [ [ 0, 1, Z(2^2)^2, 0 ], [ 1, 0, 1, 1 ], [ 1, 1, Z(2^2), 1 ], [ 1, Z(2^2), 0, 1 ], [ 1, Z(2^2)^2, Z(2^2)^2, 1 ] ], [ [ 0, 1, Z(2^2)^2, 1 ], [ 1, 0, Z(2^2), 1 ], [ 1, 1, 1, 0 ], [ 1, Z(2^2), Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2)^2, 0, Z(2^2) ] ], [ [ 0, 1, Z(2^2)^2, Z(2^2) ], [ 1, 0, Z(2^2)^2, 1 ], [ 1, 1, 0, Z(2^2)^2 ], [ 1, Z(2^2), Z(2^2), Z(2^2) ], [ 1, Z(2^2)^2, 1, 0 ] ], [ [ 0, 1, Z(2^2)^2, Z(2^2)^2 ], [ 1, 0, 0, Z(2^2) ], [ 1, 1, Z(2^2)^2, 1 ], [ 1, Z(2^2), 1, Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2), 0 ] ] ] The stabilizer of this partial spread in PGL(4,4) has size 72 and is generated by the images of the matrices: [ [ Z(2^2)^2, 0, 0, 0 ], [ 0, Z(2^2)^2, 0, 0 ], [ 0, 0, Z(2^2)^2, 0 ], [ 0, 0, 0, Z(2^2)^2 ] ], [ [ 1, Z(2^2), Z(2^2)^2, 1 ], [ 1, 1, Z(2^2)^2, Z(2^2)^2 ], [ 0, 0, 1, Z(2^2) ], [ 0, 0, 1, 1 ] ], [ [ 1, 0, 0, 0 ], [ Z(2^2), Z(2^2), 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, Z(2^2), Z(2^2) ] ], [ [ 0, 0, Z(2^2)^2, 1 ], [ 0, 0, Z(2^2)^2, Z(2^2)^2 ], [ Z(2^2), Z(2^2)^2, 0, 0 ], [ Z(2^2), Z(2^2), 0, 0 ] ], [ [ Z(2^2)^2, 1, Z(2^2), Z(2^2) ], [ 0, Z(2^2)^2, Z(2^2), Z(2^2)^2 ], [ 1, 1, 0, Z(2^2) ], [ 1, Z(2^2), Z(2^2)^2, Z(2^2) ] ], Maximal partial spread: [ [ [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ], [ 0, 0, 1, 1 ], [ 0, 0, 1, Z(2^2) ], [ 0, 0, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 1, 1, 0, 0 ], [ 1, Z(2^2), 0, 0 ], [ 1, Z(2^2)^2, 0, 0 ] ], [ [ 0, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 1, 1, 1, 1 ], [ 1, Z(2^2), 1, Z(2^2) ], [ 1, Z(2^2)^2, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, Z(2^2) ], [ 1, 0, Z(2^2), 0 ], [ 1, 1, Z(2^2), Z(2^2) ], [ 1, Z(2^2), Z(2^2), Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2), 1 ] ], [ [ 0, 1, 0, Z(2^2)^2 ], [ 1, 0, Z(2^2)^2, 0 ], [ 1, 1, Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2), Z(2^2)^2, 1 ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2) ] ], [ [ 0, 1, 1, 0 ], [ 1, 0, 1, Z(2^2) ], [ 1, 1, 0, Z(2^2) ], [ 1, Z(2^2), Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2)^2, Z(2^2), Z(2^2) ] ], [ [ 0, 1, 1, 1 ], [ 1, 0, Z(2^2), 1 ], [ 1, 1, Z(2^2)^2, 0 ], [ 1, Z(2^2), 0, Z(2^2)^2 ], [ 1, Z(2^2)^2, 1, Z(2^2) ] ], [ [ 0, 1, 1, Z(2^2) ], [ 1, 0, Z(2^2)^2, Z(2^2)^2 ], [ 1, 1, Z(2^2), 1 ], [ 1, Z(2^2), 1, 0 ], [ 1, Z(2^2)^2, 0, Z(2^2) ] ], [ [ 0, 1, 1, Z(2^2)^2 ], [ 1, 0, 0, 1 ], [ 1, 1, 1, Z(2^2) ], [ 1, Z(2^2), Z(2^2), 0 ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2)^2 ] ], [ [ 0, 1, Z(2^2), Z(2^2) ], [ 1, 0, Z(2^2)^2, Z(2^2) ], [ 1, 1, 1, 0 ], [ 1, Z(2^2), 0, 1 ], [ 1, Z(2^2)^2, Z(2^2), Z(2^2)^2 ] ], [ [ 0, 1, Z(2^2)^2, 0 ], [ 1, 0, Z(2^2)^2, 1 ], [ 1, 1, 0, 1 ], [ 1, Z(2^2), Z(2^2), 1 ], [ 1, Z(2^2)^2, 1, 1 ] ], [ [ 0, 1, Z(2^2)^2, 1 ], [ 1, 0, Z(2^2), Z(2^2) ], [ 1, 1, 1, Z(2^2)^2 ], [ 1, Z(2^2), Z(2^2)^2, 0 ], [ 1, Z(2^2)^2, 0, 1 ] ], [ [ 0, 1, Z(2^2)^2, Z(2^2) ], [ 1, 0, 1, 1 ], [ 1, 1, Z(2^2), Z(2^2)^2 ], [ 1, Z(2^2), 0, Z(2^2) ], [ 1, Z(2^2)^2, Z(2^2)^2, 0 ] ], [ [ 0, 1, Z(2^2)^2, Z(2^2)^2 ], [ 1, 0, 0, Z(2^2) ], [ 1, 1, Z(2^2)^2, 1 ], [ 1, Z(2^2), 1, Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2), 0 ] ] ] The stabilizer of this partial spread in PGL(4,4) has size 72 and is generated by the images of the matrices: [ [ Z(2^2)^2, 0, 0, 0 ], [ 0, Z(2^2)^2, 0, 0 ], [ 0, 0, Z(2^2)^2, 0 ], [ 0, 0, 0, Z(2^2)^2 ] ], [ [ 0, Z(2^2), 0, Z(2^2) ], [ 1, 0, 1, 0 ], [ 0, 0, 0, Z(2^2) ], [ 0, 0, 1, 0 ] ], [ [ 0, Z(2^2), 0, 0 ], [ 1, Z(2^2)^2, 0, 0 ], [ 0, 0, 0, Z(2^2) ], [ 0, 0, 1, Z(2^2)^2 ] ], [ [ Z(2^2), 1, Z(2^2), 1 ], [ Z(2^2)^2, 0, Z(2^2)^2, 0 ], [ Z(2^2), 1, 0, 0 ], [ Z(2^2)^2, 0, 0, 0 ] ], [ [ Z(2^2), Z(2^2), Z(2^2)^2, 1 ], [ Z(2^2), Z(2^2)^2, 0, Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2), Z(2^2) ], [ Z(2^2), 0, Z(2^2), Z(2^2)^2 ] ], Maximal partial spread: [ [ [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ], [ 0, 0, 1, 1 ], [ 0, 0, 1, Z(2^2) ], [ 0, 0, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 1, 1, 0, 0 ], [ 1, Z(2^2), 0, 0 ], [ 1, Z(2^2)^2, 0, 0 ] ], [ [ 0, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 1, 1, 1, 1 ], [ 1, Z(2^2), 1, Z(2^2) ], [ 1, Z(2^2)^2, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, Z(2^2) ], [ 1, 0, Z(2^2), 0 ], [ 1, 1, Z(2^2), Z(2^2) ], [ 1, Z(2^2), Z(2^2), Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2), 1 ] ], [ [ 0, 1, 0, Z(2^2)^2 ], [ 1, 0, Z(2^2)^2, 1 ], [ 1, 1, Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2), Z(2^2)^2, 0 ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2)^2 ] ], [ [ 0, 1, 1, 0 ], [ 1, 0, 0, Z(2^2) ], [ 1, 1, 1, Z(2^2) ], [ 1, Z(2^2), Z(2^2), Z(2^2) ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2) ] ], [ [ 0, 1, Z(2^2), 0 ], [ 1, 0, Z(2^2), 1 ], [ 1, 1, 0, 1 ], [ 1, Z(2^2), 1, 1 ], [ 1, Z(2^2)^2, Z(2^2)^2, 1 ] ], [ [ 0, 1, Z(2^2), 1 ], [ 1, 0, 0, 1 ], [ 1, 1, Z(2^2), 0 ], [ 1, Z(2^2), Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2)^2, 1, Z(2^2) ] ], [ [ 0, 1, Z(2^2), Z(2^2) ], [ 1, 0, 1, Z(2^2)^2 ], [ 1, 1, Z(2^2)^2, 1 ], [ 1, Z(2^2), Z(2^2), 0 ], [ 1, Z(2^2)^2, 0, Z(2^2) ] ], [ [ 0, 1, Z(2^2), Z(2^2)^2 ], [ 1, 0, Z(2^2)^2, 0 ], [ 1, 1, 1, Z(2^2)^2 ], [ 1, Z(2^2), 0, 1 ], [ 1, Z(2^2)^2, Z(2^2), Z(2^2) ] ], [ [ 0, 1, Z(2^2)^2, 0 ], [ 1, 0, 0, Z(2^2)^2 ], [ 1, 1, Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2), 1, Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2), Z(2^2)^2 ] ], [ [ 0, 1, Z(2^2)^2, 1 ], [ 1, 0, Z(2^2)^2, Z(2^2)^2 ], [ 1, 1, 0, Z(2^2) ], [ 1, Z(2^2), Z(2^2), 1 ], [ 1, Z(2^2)^2, 1, 0 ] ], [ [ 0, 1, Z(2^2)^2, Z(2^2) ], [ 1, 0, 1, 1 ], [ 1, 1, Z(2^2), Z(2^2)^2 ], [ 1, Z(2^2), 0, Z(2^2) ], [ 1, Z(2^2)^2, Z(2^2)^2, 0 ] ], [ [ 0, 1, Z(2^2)^2, Z(2^2)^2 ], [ 1, 0, Z(2^2), Z(2^2)^2 ], [ 1, 1, 1, 0 ], [ 1, Z(2^2), Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2)^2, 0, 1 ] ] ] The stabilizer of this partial spread in PGL(4,4) has size 168 and is generated by the images of the matrices: [ [ Z(2^2)^2, 0, 0, 0 ], [ 0, Z(2^2)^2, 0, 0 ], [ 0, 0, Z(2^2)^2, 0 ], [ 0, 0, 0, Z(2^2)^2 ] ], [ [ 1, 0, Z(2^2)^2, 1 ], [ Z(2^2)^2, Z(2^2)^2, Z(2^2), 1 ], [ 0, 0, 1, 0 ], [ 0, 0, Z(2^2), Z(2^2) ] ], [ [ 0, 1, Z(2^2)^2, 0 ], [ Z(2^2)^2, 0, 0, Z(2^2) ], [ 0, 0, 0, Z(2^2)^2 ], [ 0, 0, 1, 0 ] ], [ [ Z(2^2), Z(2^2)^2, 0, Z(2^2) ], [ Z(2^2), Z(2^2), Z(2^2), 1 ], [ 0, 1, 0, 0 ], [ Z(2^2)^2, Z(2^2), 0, 0 ] ], Maximal partial spread: [ [ [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ], [ 0, 0, 1, 1 ], [ 0, 0, 1, Z(2^2) ], [ 0, 0, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 1, 1, 0, 0 ], [ 1, Z(2^2), 0, 0 ], [ 1, Z(2^2)^2, 0, 0 ] ], [ [ 0, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 1, 1, 1, 1 ], [ 1, Z(2^2), 1, Z(2^2) ], [ 1, Z(2^2)^2, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, Z(2^2) ], [ 1, 0, Z(2^2), 0 ], [ 1, 1, Z(2^2), Z(2^2) ], [ 1, Z(2^2), Z(2^2), Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2), 1 ] ], [ [ 0, 1, 0, Z(2^2)^2 ], [ 1, 0, Z(2^2)^2, 1 ], [ 1, 1, Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2), Z(2^2)^2, 0 ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2)^2 ] ], [ [ 0, 1, 1, 0 ], [ 1, 0, 1, Z(2^2) ], [ 1, 1, 0, Z(2^2) ], [ 1, Z(2^2), Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2)^2, Z(2^2), Z(2^2) ] ], [ [ 0, 1, 1, 1 ], [ 1, 0, 0, Z(2^2)^2 ], [ 1, 1, 1, Z(2^2) ], [ 1, Z(2^2), Z(2^2), 1 ], [ 1, Z(2^2)^2, Z(2^2)^2, 0 ] ], [ [ 0, 1, 1, Z(2^2)^2 ], [ 1, 0, Z(2^2)^2, 0 ], [ 1, 1, Z(2^2), Z(2^2)^2 ], [ 1, Z(2^2), 1, 1 ], [ 1, Z(2^2)^2, 0, Z(2^2) ] ], [ [ 0, 1, Z(2^2), 0 ], [ 1, 0, Z(2^2)^2, Z(2^2)^2 ], [ 1, 1, 1, Z(2^2)^2 ], [ 1, Z(2^2), 0, Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2), Z(2^2)^2 ] ], [ [ 0, 1, Z(2^2), Z(2^2) ], [ 1, 0, Z(2^2), Z(2^2)^2 ], [ 1, 1, 0, 1 ], [ 1, Z(2^2), 1, 0 ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2) ] ], [ [ 0, 1, Z(2^2), Z(2^2)^2 ], [ 1, 0, 0, Z(2^2) ], [ 1, 1, Z(2^2), 1 ], [ 1, Z(2^2), Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2)^2, 1, 0 ] ], [ [ 0, 1, Z(2^2)^2, 1 ], [ 1, 0, Z(2^2)^2, Z(2^2) ], [ 1, 1, 0, Z(2^2)^2 ], [ 1, Z(2^2), Z(2^2), 0 ], [ 1, Z(2^2)^2, 1, 1 ] ], [ [ 0, 1, Z(2^2)^2, Z(2^2) ], [ 1, 0, Z(2^2), Z(2^2) ], [ 1, 1, 1, 0 ], [ 1, Z(2^2), Z(2^2)^2, 1 ], [ 1, Z(2^2)^2, 0, Z(2^2)^2 ] ], [ [ 0, 1, Z(2^2)^2, Z(2^2)^2 ], [ 1, 0, 1, Z(2^2)^2 ], [ 1, 1, Z(2^2), 0 ], [ 1, Z(2^2), 0, Z(2^2) ], [ 1, Z(2^2)^2, Z(2^2)^2, 1 ] ] ] The stabilizer of this partial spread in PGL(4,4) has size 168 and is generated by the images of the matrices: [ [ Z(2^2)^2, 0, 0, 0 ], [ 0, Z(2^2)^2, 0, 0 ], [ 0, 0, Z(2^2)^2, 0 ], [ 0, 0, 0, Z(2^2)^2 ] ], [ [ Z(2^2), 0, Z(2^2)^2, Z(2^2)^2 ], [ Z(2^2)^2, 1, Z(2^2), Z(2^2)^2 ], [ 0, 0, Z(2^2)^2, 0 ], [ 0, 0, 0, 1 ] ], [ [ Z(2^2)^2, Z(2^2), 0, 1 ], [ 1, 0, Z(2^2)^2, 0 ], [ 0, 0, Z(2^2)^2, Z(2^2) ], [ 0, 0, 0, Z(2^2) ] ], [ [ Z(2^2), Z(2^2), Z(2^2)^2, 1 ], [ Z(2^2)^2, 0, Z(2^2), 0 ], [ Z(2^2)^2, 1, 0, 0 ], [ Z(2^2), 1, 0, 0 ] ], THE 3 INEQUIVALENT MAXIMAL PARTIAL SPREAD(S) OF SIZE 17: Maximal partial spread: [ [ [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ], [ 0, 0, 1, 1 ], [ 0, 0, 1, Z(2^2) ], [ 0, 0, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 1, 1, 0, 0 ], [ 1, Z(2^2), 0, 0 ], [ 1, Z(2^2)^2, 0, 0 ] ], [ [ 0, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 1, 1, 1, 1 ], [ 1, Z(2^2), 1, Z(2^2) ], [ 1, Z(2^2)^2, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, Z(2^2) ], [ 1, 0, Z(2^2), 0 ], [ 1, 1, Z(2^2), Z(2^2) ], [ 1, Z(2^2), Z(2^2), Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2), 1 ] ], [ [ 0, 1, 0, Z(2^2)^2 ], [ 1, 0, Z(2^2)^2, 0 ], [ 1, 1, Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2), Z(2^2)^2, 1 ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2) ] ], [ [ 0, 1, 1, 0 ], [ 1, 0, 1, Z(2^2) ], [ 1, 1, 0, Z(2^2) ], [ 1, Z(2^2), Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2)^2, Z(2^2), Z(2^2) ] ], [ [ 0, 1, 1, 1 ], [ 1, 0, 0, Z(2^2) ], [ 1, 1, 1, Z(2^2)^2 ], [ 1, Z(2^2), Z(2^2), 0 ], [ 1, Z(2^2)^2, Z(2^2)^2, 1 ] ], [ [ 0, 1, 1, Z(2^2) ], [ 1, 0, Z(2^2)^2, Z(2^2) ], [ 1, 1, Z(2^2), 0 ], [ 1, Z(2^2), 1, 1 ], [ 1, Z(2^2)^2, 0, Z(2^2)^2 ] ], [ [ 0, 1, 1, Z(2^2)^2 ], [ 1, 0, Z(2^2), Z(2^2) ], [ 1, 1, Z(2^2)^2, 1 ], [ 1, Z(2^2), 0, Z(2^2)^2 ], [ 1, Z(2^2)^2, 1, 0 ] ], [ [ 0, 1, Z(2^2), 0 ], [ 1, 0, Z(2^2), Z(2^2)^2 ], [ 1, 1, 0, Z(2^2)^2 ], [ 1, Z(2^2), 1, Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2)^2 ] ], [ [ 0, 1, Z(2^2), 1 ], [ 1, 0, Z(2^2)^2, Z(2^2)^2 ], [ 1, 1, 1, Z(2^2) ], [ 1, Z(2^2), 0, 1 ], [ 1, Z(2^2)^2, Z(2^2), 0 ] ], [ [ 0, 1, Z(2^2), Z(2^2) ], [ 1, 0, 0, Z(2^2)^2 ], [ 1, 1, Z(2^2), 1 ], [ 1, Z(2^2), Z(2^2)^2, 0 ], [ 1, Z(2^2)^2, 1, Z(2^2) ] ], [ [ 0, 1, Z(2^2), Z(2^2)^2 ], [ 1, 0, 1, Z(2^2)^2 ], [ 1, 1, Z(2^2)^2, 0 ], [ 1, Z(2^2), Z(2^2), Z(2^2) ], [ 1, Z(2^2)^2, 0, 1 ] ], [ [ 0, 1, Z(2^2)^2, 0 ], [ 1, 0, Z(2^2)^2, 1 ], [ 1, 1, 0, 1 ], [ 1, Z(2^2), Z(2^2), 1 ], [ 1, Z(2^2)^2, 1, 1 ] ], [ [ 0, 1, Z(2^2)^2, 1 ], [ 1, 0, Z(2^2), 1 ], [ 1, 1, 1, 0 ], [ 1, Z(2^2), Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2)^2, 0, Z(2^2) ] ], [ [ 0, 1, Z(2^2)^2, Z(2^2) ], [ 1, 0, 1, 1 ], [ 1, 1, Z(2^2), Z(2^2)^2 ], [ 1, Z(2^2), 0, Z(2^2) ], [ 1, Z(2^2)^2, Z(2^2)^2, 0 ] ], [ [ 0, 1, Z(2^2)^2, Z(2^2)^2 ], [ 1, 0, 0, 1 ], [ 1, 1, Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2), 1, 0 ], [ 1, Z(2^2)^2, Z(2^2), Z(2^2)^2 ] ] ] The stabilizer of this partial spread in PGL(4,4) has size 40800 and is generated by the images of the matrices: [ [ Z(2^2)^2, 0, 0, 0 ], [ 0, Z(2^2)^2, 0, 0 ], [ 0, 0, Z(2^2)^2, 0 ], [ 0, 0, 0, Z(2^2)^2 ] ], [ [ 1, Z(2^2), 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 1, Z(2^2) ], [ 0, 0, 1, 0 ] ], [ [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2) ], [ 1, 1, Z(2^2)^2, Z(2^2)^2 ], [ 0, 0, 1, Z(2^2)^2 ], [ 0, 0, 1, 1 ] ], [ [ Z(2^2), Z(2^2), 0, Z(2^2) ], [ 0, Z(2^2), 1, 0 ], [ 0, 0, 1, Z(2^2)^2 ], [ 0, 0, 1, 1 ] ], [ [ 1, Z(2^2)^2, 1, 1 ], [ 1, 1, 0, 1 ], [ 0, 0, 1, Z(2^2)^2 ], [ 0, 0, 1, 1 ] ], [ [ Z(2^2), Z(2^2), Z(2^2), 1 ], [ 0, Z(2^2), Z(2^2), Z(2^2) ], [ Z(2^2), 1, 0, 0 ], [ Z(2^2), Z(2^2), 0, 0 ] ], Maximal partial spread: [ [ [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ], [ 0, 0, 1, 1 ], [ 0, 0, 1, Z(2^2) ], [ 0, 0, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 1, 1, 0, 0 ], [ 1, Z(2^2), 0, 0 ], [ 1, Z(2^2)^2, 0, 0 ] ], [ [ 0, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 1, 1, 1, 1 ], [ 1, Z(2^2), 1, Z(2^2) ], [ 1, Z(2^2)^2, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, Z(2^2) ], [ 1, 0, Z(2^2), 0 ], [ 1, 1, Z(2^2), Z(2^2) ], [ 1, Z(2^2), Z(2^2), Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2), 1 ] ], [ [ 0, 1, 0, Z(2^2)^2 ], [ 1, 0, Z(2^2)^2, 0 ], [ 1, 1, Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2), Z(2^2)^2, 1 ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2) ] ], [ [ 0, 1, 1, 0 ], [ 1, 0, 1, Z(2^2) ], [ 1, 1, 0, Z(2^2) ], [ 1, Z(2^2), Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2)^2, Z(2^2), Z(2^2) ] ], [ [ 0, 1, 1, 1 ], [ 1, 0, 0, Z(2^2) ], [ 1, 1, 1, Z(2^2)^2 ], [ 1, Z(2^2), Z(2^2), 0 ], [ 1, Z(2^2)^2, Z(2^2)^2, 1 ] ], [ [ 0, 1, 1, Z(2^2) ], [ 1, 0, Z(2^2)^2, Z(2^2) ], [ 1, 1, Z(2^2), 0 ], [ 1, Z(2^2), 1, 1 ], [ 1, Z(2^2)^2, 0, Z(2^2)^2 ] ], [ [ 0, 1, 1, Z(2^2)^2 ], [ 1, 0, Z(2^2), Z(2^2)^2 ], [ 1, 1, Z(2^2)^2, 0 ], [ 1, Z(2^2), 0, Z(2^2) ], [ 1, Z(2^2)^2, 1, 1 ] ], [ [ 0, 1, Z(2^2), 0 ], [ 1, 0, 1, 1 ], [ 1, 1, Z(2^2)^2, 1 ], [ 1, Z(2^2), Z(2^2), 1 ], [ 1, Z(2^2)^2, 0, 1 ] ], [ [ 0, 1, Z(2^2), 1 ], [ 1, 0, Z(2^2)^2, Z(2^2)^2 ], [ 1, 1, 1, Z(2^2) ], [ 1, Z(2^2), 0, 1 ], [ 1, Z(2^2)^2, Z(2^2), 0 ] ], [ [ 0, 1, Z(2^2), Z(2^2) ], [ 1, 0, 0, Z(2^2)^2 ], [ 1, 1, Z(2^2), 1 ], [ 1, Z(2^2), Z(2^2)^2, 0 ], [ 1, Z(2^2)^2, 1, Z(2^2) ] ], [ [ 0, 1, Z(2^2), Z(2^2)^2 ], [ 1, 0, Z(2^2), Z(2^2) ], [ 1, 1, 0, 1 ], [ 1, Z(2^2), 1, Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2)^2, 0 ] ], [ [ 0, 1, Z(2^2)^2, 0 ], [ 1, 0, 1, Z(2^2)^2 ], [ 1, 1, Z(2^2), Z(2^2)^2 ], [ 1, Z(2^2), 0, Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2)^2 ] ], [ [ 0, 1, Z(2^2)^2, 1 ], [ 1, 0, Z(2^2), 1 ], [ 1, 1, 1, 0 ], [ 1, Z(2^2), Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2)^2, 0, Z(2^2) ] ], [ [ 0, 1, Z(2^2)^2, Z(2^2) ], [ 1, 0, Z(2^2)^2, 1 ], [ 1, 1, 0, Z(2^2)^2 ], [ 1, Z(2^2), Z(2^2), Z(2^2) ], [ 1, Z(2^2)^2, 1, 0 ] ], [ [ 0, 1, Z(2^2)^2, Z(2^2)^2 ], [ 1, 0, 0, 1 ], [ 1, 1, Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2), 1, 0 ], [ 1, Z(2^2)^2, Z(2^2), Z(2^2)^2 ] ] ] The stabilizer of this partial spread in PGL(4,4) has size 600 and is generated by the images of the matrices: [ [ Z(2^2)^2, 0, 0, 0 ], [ 0, Z(2^2)^2, 0, 0 ], [ 0, 0, Z(2^2)^2, 0 ], [ 0, 0, 0, Z(2^2)^2 ] ], [ [ 1, Z(2^2), 0, 1 ], [ Z(2^2), 1, Z(2^2)^2, 0 ], [ 0, 0, 1, Z(2^2)^2 ], [ 0, 0, 1, 1 ] ], [ [ Z(2^2)^2, Z(2^2)^2, Z(2^2)^2, 1 ], [ 0, Z(2^2)^2, 1, Z(2^2)^2 ], [ 0, 0, 0, Z(2^2) ], [ 0, 0, 1, 0 ] ], [ [ 0, 1, 0, 0 ], [ Z(2^2)^2, 0, 0, 0 ], [ 0, 0, Z(2^2), Z(2^2) ], [ 0, 0, 0, Z(2^2) ] ], [ [ 0, 0, 0, Z(2^2)^2 ], [ 0, 0, Z(2^2), Z(2^2) ], [ Z(2^2)^2, 0, 0, 0 ], [ 0, Z(2^2)^2, 0, 0 ] ], Maximal partial spread: [ [ [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ], [ 0, 0, 1, 1 ], [ 0, 0, 1, Z(2^2) ], [ 0, 0, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 1, 1, 0, 0 ], [ 1, Z(2^2), 0, 0 ], [ 1, Z(2^2)^2, 0, 0 ] ], [ [ 0, 1, 0, 1 ], [ 1, 0, 1, 0 ], [ 1, 1, 1, 1 ], [ 1, Z(2^2), 1, Z(2^2) ], [ 1, Z(2^2)^2, 1, Z(2^2)^2 ] ], [ [ 0, 1, 0, Z(2^2) ], [ 1, 0, Z(2^2), 0 ], [ 1, 1, Z(2^2), Z(2^2) ], [ 1, Z(2^2), Z(2^2), Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2), 1 ] ], [ [ 0, 1, 0, Z(2^2)^2 ], [ 1, 0, Z(2^2)^2, 1 ], [ 1, 1, Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2), Z(2^2)^2, 0 ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2)^2 ] ], [ [ 0, 1, 1, 0 ], [ 1, 0, 0, Z(2^2) ], [ 1, 1, 1, Z(2^2) ], [ 1, Z(2^2), Z(2^2), Z(2^2) ], [ 1, Z(2^2)^2, Z(2^2)^2, Z(2^2) ] ], [ [ 0, 1, 1, 1 ], [ 1, 0, 1, Z(2^2)^2 ], [ 1, 1, 0, Z(2^2) ], [ 1, Z(2^2), Z(2^2)^2, 1 ], [ 1, Z(2^2)^2, Z(2^2), 0 ] ], [ [ 0, 1, 1, Z(2^2) ], [ 1, 0, Z(2^2), 1 ], [ 1, 1, Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2), 0, Z(2^2) ], [ 1, Z(2^2)^2, 1, 0 ] ], [ [ 0, 1, 1, Z(2^2)^2 ], [ 1, 0, Z(2^2)^2, 0 ], [ 1, 1, Z(2^2), Z(2^2)^2 ], [ 1, Z(2^2), 1, 1 ], [ 1, Z(2^2)^2, 0, Z(2^2) ] ], [ [ 0, 1, Z(2^2), 0 ], [ 1, 0, 1, 1 ], [ 1, 1, Z(2^2)^2, 1 ], [ 1, Z(2^2), Z(2^2), 1 ], [ 1, Z(2^2)^2, 0, 1 ] ], [ [ 0, 1, Z(2^2), 1 ], [ 1, 0, Z(2^2), Z(2^2) ], [ 1, 1, 0, Z(2^2)^2 ], [ 1, Z(2^2), 1, 0 ], [ 1, Z(2^2)^2, Z(2^2)^2, 1 ] ], [ [ 0, 1, Z(2^2), Z(2^2) ], [ 1, 0, Z(2^2)^2, Z(2^2) ], [ 1, 1, 1, 0 ], [ 1, Z(2^2), 0, 1 ], [ 1, Z(2^2)^2, Z(2^2), Z(2^2)^2 ] ], [ [ 0, 1, Z(2^2), Z(2^2)^2 ], [ 1, 0, 0, Z(2^2)^2 ], [ 1, 1, Z(2^2), 0 ], [ 1, Z(2^2), Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2)^2, 1, 1 ] ], [ [ 0, 1, Z(2^2)^2, 0 ], [ 1, 0, Z(2^2), Z(2^2)^2 ], [ 1, 1, 1, Z(2^2)^2 ], [ 1, Z(2^2), Z(2^2)^2, Z(2^2)^2 ], [ 1, Z(2^2)^2, 0, Z(2^2)^2 ] ], [ [ 0, 1, Z(2^2)^2, 1 ], [ 1, 0, 0, 1 ], [ 1, 1, Z(2^2)^2, 0 ], [ 1, Z(2^2), 1, Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2), Z(2^2) ] ], [ [ 0, 1, Z(2^2)^2, Z(2^2) ], [ 1, 0, Z(2^2)^2, Z(2^2)^2 ], [ 1, 1, 0, 1 ], [ 1, Z(2^2), Z(2^2), 0 ], [ 1, Z(2^2)^2, 1, Z(2^2) ] ], [ [ 0, 1, Z(2^2)^2, Z(2^2)^2 ], [ 1, 0, 1, Z(2^2) ], [ 1, 1, Z(2^2), 1 ], [ 1, Z(2^2), 0, Z(2^2)^2 ], [ 1, Z(2^2)^2, Z(2^2)^2, 0 ] ] ] The stabilizer of this partial spread in PGL(4,4) has size 288 and is generated by the images of the matrices: [ [ Z(2^2)^2, 0, 0, 0 ], [ 0, Z(2^2)^2, 0, 0 ], [ 0, 0, Z(2^2)^2, 0 ], [ 0, 0, 0, Z(2^2)^2 ] ], [ [ Z(2^2), 0, 0, 0 ], [ 1, Z(2^2)^2, 0, 0 ], [ 0, 0, 0, 1 ], [ 0, 0, 1, 1 ] ], [ [ Z(2^2)^2, Z(2^2)^2, Z(2^2)^2, Z(2^2) ], [ 1, Z(2^2)^2, 0, Z(2^2)^2 ], [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ] ], [ [ 1, 1, Z(2^2), 1 ], [ 0, 1, Z(2^2)^2, Z(2^2)^2 ], [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ] ], [ [ Z(2^2)^2, 0, Z(2^2)^2, 1 ], [ 0, Z(2^2)^2, Z(2^2), Z(2^2) ], [ 1, Z(2^2)^2, 0, 0 ], [ 1, Z(2^2), 0, 0 ] ], [ [ 1, Z(2^2)^2, 0, 1 ], [ 1, Z(2^2), Z(2^2), 1 ], [ 1, Z(2^2)^2, 1, Z(2^2)^2 ], [ 1, Z(2^2), 1, Z(2^2) ] ], gap> Runtime(); 191987120 gap>