This page contains a collection of t-designs, with an
emphasis on balanced incomplete-block designs
(equivalently 2-(v,k,lambda) designs with k<v).
The files downloadable from this page contain lists of pairwise
non-isomorphic t-designs for the given parameters t,v,b,r,k,L(=lambda).
They are in DTRS
external representation protocol version 2.0 format,
compressed by bzip2. Each file has content types i, c, g and s, which
mean that each design in that file has, respectively,
`<indicators>`, `<combinatorial_properties>`,
`<automorphism_group>` and
`<statistical_properties>` subtrees. Certain files also
have content type a, which means that **all** t-designs (up to
isomorphism) with the given parameters are in that file.
For each resolvable t-design in the files on this page, at least one
resolution is given.

For 6<=v<=20, r<=20 and 3<=k<=v/2, we give at least one design for each parameter list (2,v,b,r,k,L) for which a 2-design exists. Moreover, for these parameters, we include, up to isomorphism, at least all cyclic and all 1-rotational 2-designs.

In addition, we give the projective planes PG(2,q) for
q=4,5,7,8, the affine planes AG(2,q) for q=5,7,8, the cyclic and
the 1-rotational 2-(v,3,1) designs for 21<=v<=31,
the cyclic and the 1-rotational 2-(21,4,3) designs,
the cyclic and the 1-rotational 2-(22,4,2) designs,
the 2-(31,4,2) designs invariant under a group of order 93,
the 5-(12,6,1),
4-(11,5,1) and 3-(10,4,1) designs associated with the small Mathieu
group M_{12}, and the 5-(24,8,1), 4-(23,7,1) and 3-(22,6,1)
designs associated with the large Mathieu group M_{24}.

No particular ordering of designs within a file should be assumed.

**Note:**
The naming and ordering of designs and some isomorphism class
representatives changed when this page was overhauled
on 25 November 2004.

**Number of files = 99**

t | v | b | r | k | L | content type | # designs | |
---|---|---|---|---|---|---|---|---|

2 | 6 | 10 | 5 | 3 | 2 | i c g s a | 1 | download |

2 | 6 | 20 | 10 | 3 | 4 | i c g s a | 4 | download |

2 | 6 | 30 | 15 | 3 | 6 | i c g s a | 6 | download |

2 | 6 | 40 | 20 | 3 | 8 | i c g s a | 13 | download |

2 | 7 | 7 | 3 | 3 | 1 | i c g s a | 1 | download |

2 | 7 | 14 | 6 | 3 | 2 | i c g s a | 4 | download |

2 | 7 | 21 | 9 | 3 | 3 | i c g s a | 10 | download |

2 | 7 | 28 | 12 | 3 | 4 | i c g s a | 35 | download |

2 | 7 | 35 | 15 | 3 | 5 | i c g s a | 109 | download |

2 | 7 | 42 | 18 | 3 | 6 | i c g s a | 418 | download |

2 | 8 | 14 | 7 | 4 | 3 | i c g s a | 4 | download |

2 | 8 | 28 | 14 | 4 | 6 | i c g s a | 2310 | download |

2 | 9 | 12 | 4 | 3 | 1 | i c g s a | 1 | download |

t | v | b | r | k | L | content type | # designs | |

2 | 9 | 18 | 8 | 4 | 3 | i c g s a | 11 | download |

2 | 9 | 24 | 8 | 3 | 2 | i c g s a | 36 | download |

2 | 9 | 36 | 12 | 3 | 3 | i c g s | 9 | download |

2 | 9 | 36 | 16 | 4 | 6 | i c g s | 31 | download |

2 | 9 | 48 | 16 | 3 | 4 | i c g s | 19 | download |

2 | 9 | 60 | 20 | 3 | 5 | i c g s | 28 | download |

2 | 10 | 15 | 6 | 4 | 2 | i c g s a | 3 | download |

2 | 10 | 18 | 9 | 5 | 4 | i c g s | 2 | download |

2 | 10 | 30 | 9 | 3 | 2 | i c g s a | 960 | download |

2 | 10 | 30 | 12 | 4 | 4 | i c g s | 13 | download |

2 | 10 | 36 | 18 | 5 | 8 | i c g s | 40 | download |

2 | 10 | 45 | 18 | 4 | 6 | i c g s | 105 | download |

2 | 10 | 60 | 18 | 3 | 4 | i c g s | 30 | download |

t | v | b | r | k | L | content type | # designs | |

2 | 11 | 11 | 5 | 5 | 2 | i c g s a | 1 | download |

2 | 11 | 22 | 10 | 5 | 4 | i c g s | 7 | download |

2 | 11 | 33 | 15 | 5 | 6 | i c g s | 11 | download |

2 | 11 | 44 | 20 | 5 | 8 | i c g s | 151 | download |

2 | 11 | 55 | 15 | 3 | 3 | i c g s | 21 | download |

2 | 11 | 55 | 20 | 4 | 6 | i c g s | 348 | download |

2 | 12 | 22 | 11 | 6 | 5 | i c g s | 5 | download |

2 | 12 | 33 | 11 | 4 | 3 | i c g s | 10 | download |

2 | 12 | 44 | 11 | 3 | 2 | i c g s | 9 | download |

2 | 13 | 13 | 4 | 4 | 1 | i c g s a | 1 | download |

2 | 13 | 26 | 6 | 3 | 1 | i c g s a | 2 | download |

2 | 13 | 26 | 8 | 4 | 2 | i c g s | 4 | download |

2 | 13 | 26 | 12 | 6 | 5 | i c g s | 7 | download |

t | v | b | r | k | L | content type | # designs | |

2 | 13 | 39 | 12 | 4 | 3 | i c g s | 26 | download |

2 | 13 | 39 | 15 | 5 | 5 | i c g s | 76 | download |

2 | 13 | 52 | 12 | 3 | 2 | i c g s | 21 | download |

2 | 13 | 52 | 16 | 4 | 4 | i c g s | 294 | download |

2 | 13 | 65 | 20 | 4 | 5 | i c g s | 571 | download |

2 | 13 | 78 | 18 | 3 | 3 | i c g s | 152 | download |

2 | 14 | 26 | 13 | 7 | 6 | i c g s | 7 | download |

2 | 15 | 15 | 7 | 7 | 3 | i c g s a | 5 | download |

2 | 15 | 30 | 14 | 7 | 6 | i c g s | 31 | download |

2 | 15 | 35 | 7 | 3 | 1 | i c g s a | 80 | download |

2 | 15 | 35 | 14 | 6 | 5 | i c g s | 8 | download |

2 | 15 | 42 | 14 | 5 | 4 | i c g s | 85 | download |

2 | 15 | 70 | 14 | 3 | 2 | i c g s | 62 | download |

t | v | b | r | k | L | content type | # designs | |

2 | 16 | 16 | 6 | 6 | 2 | i c g s a | 3 | download |

2 | 16 | 20 | 5 | 4 | 1 | i c g s a | 1 | download |

2 | 16 | 24 | 9 | 6 | 3 | i c g s | 1 | download |

2 | 16 | 30 | 15 | 8 | 7 | i c g s | 24 | download |

2 | 16 | 32 | 12 | 6 | 4 | i c g s | 16 | download |

2 | 16 | 40 | 10 | 4 | 2 | i c g s | 6 | download |

2 | 16 | 40 | 15 | 6 | 5 | i c g s | 25 | download |

2 | 16 | 48 | 15 | 5 | 4 | i c g s | 294 | download |

2 | 16 | 48 | 18 | 6 | 6 | i c g s | 776 | download |

2 | 16 | 60 | 15 | 4 | 3 | i c g s | 450 | download |

2 | 16 | 80 | 15 | 3 | 2 | i c g s | 122 | download |

2 | 16 | 80 | 20 | 4 | 4 | i c g s | 5872 | download |

2 | 17 | 34 | 16 | 8 | 7 | i c g s | 28 | download |

t | v | b | r | k | L | content type | # designs | |

2 | 17 | 68 | 16 | 4 | 3 | i c g s | 542 | download |

2 | 17 | 68 | 20 | 5 | 5 | i c g s | 7260 | download |

2 | 18 | 34 | 17 | 9 | 8 | i c g s | 21 | download |

2 | 18 | 51 | 17 | 6 | 5 | i c g s | 582 | download |

2 | 18 | 102 | 17 | 3 | 2 | i c g s | 186 | download |

2 | 19 | 19 | 9 | 9 | 4 | i c g s a | 6 | download |

2 | 19 | 38 | 18 | 9 | 8 | i c g s | 108 | download |

2 | 19 | 57 | 9 | 3 | 1 | i c g s | 4 | download |

2 | 19 | 57 | 12 | 4 | 2 | i c g s | 22 | download |

2 | 19 | 57 | 18 | 6 | 5 | i c g s | 1535 | download |

2 | 19 | 114 | 18 | 3 | 2 | i c g s | 665 | download |

2 | 20 | 38 | 19 | 10 | 9 | i c g s | 32 | download |

2 | 20 | 76 | 19 | 5 | 4 | i c g s | 10067 | download |

t | v | b | r | k | L | content type | # designs | |

2 | 20 | 95 | 19 | 4 | 3 | i c g s | 10040 | download |

2 | 21 | 21 | 5 | 5 | 1 | i c g s a | 1 | download |

2 | 21 | 70 | 10 | 3 | 1 | i c g s | 7 | download |

2 | 21 | 105 | 20 | 4 | 3 | i c g s | 26320 | download |

2 | 22 | 77 | 14 | 4 | 2 | i c g s | 43 | download |

2 | 25 | 30 | 6 | 5 | 1 | i c g s a | 1 | download |

2 | 25 | 100 | 12 | 3 | 1 | i c g s | 12 | download |

2 | 27 | 117 | 13 | 3 | 1 | i c g s | 44 | download |

2 | 31 | 31 | 6 | 6 | 1 | i c g s a | 1 | download |

2 | 31 | 155 | 15 | 3 | 1 | i c g s | 80 | download |

2 | 31 | 155 | 20 | 4 | 2 | i c g s | 43 | download |

2 | 49 | 56 | 8 | 7 | 1 | i c g s a | 1 | download |

2 | 57 | 57 | 8 | 8 | 1 | i c g s a | 1 | download |

t | v | b | r | k | L | content type | # designs | |

2 | 64 | 72 | 9 | 8 | 1 | i c g s a | 1 | download |

2 | 73 | 73 | 9 | 9 | 1 | i c g s a | 1 | download |

3 | 10 | 30 | 12 | 4 | 1 | i c g s a | 1 | download |

3 | 22 | 77 | 21 | 6 | 1 | i c g s a | 1 | download |

4 | 11 | 66 | 30 | 5 | 1 | i c g s a | 1 | download |

4 | 23 | 253 | 77 | 7 | 1 | i c g s a | 1 | download |

5 | 12 | 132 | 66 | 6 | 1 | i c g s a | 1 | download |

5 | 24 | 759 | 253 | 8 | 1 | i c g s a | 1 | download |

Last updated: 2005-07-22 07:49:36.406216