The quality of incomplete-block designs is commonly assessed by the A-, D-, and E-optimality criteria. If there exists a balanced incomplete-block design for the given parameters, then it is optimal on all these criteria. It is therefore natural to use the proxy criteria of (almost) equal replication and (almost) equal concurrences when choosing a block design.
However, work over the last decade for block size 2 has shown that when the number of blocks is near the lower limit for estimability of all treatment contrasts then the D-criterion favours very different designs from the A- and E-criteria. In fact, the A- and E-optimal designs are far from equi-replicate and are amongst the worst on the D-criterion.
I shall report on current work which extends these results to all block sizes. Thus the problem is not blocks of size 2; it is low replication.