Optimal designs under dependence are usually difficult to specify in general, and can be highly specific to the dependence structure and the parameter value. If the number of blocks is sufficient for a semi-balanced array to exist, an incomplete block design formed from it can have some general optimality properties, which appear to be very strong. However, non-binary designs can sometimes be better. In this paper, blocks of size 3 to 6 are considered in detail, and some further results given for general block sizes. Negative dependence and extended blocks are also considered. It is shown that a rich variety of optimal designs is possible.
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