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Optimal regular graph designs. (English) Zbl 1384.62280
Summary: A typical problem in optimal design theory is finding an experimental design that is optimal with respect to some criteria in a class of designs. The most popular criteria include the $$A$$- and $$D$$-criteria. Regular graph designs occur in many optimality results, and if the number of blocks is large enough, an $$A$$-optimal (or $$D$$-optimal) design is among them (if any exist). To explore the landscape of designs with a large number of blocks, we introduce extensions of regular graph designs. These are constructed by adding the blocks of a balanced incomplete block design repeatedly to the original design. We present the results of an exact computer search for the best regular graph designs and the best extended regular graph designs with up to 20 treatments $$v$$, block size $$k \leq 10$$ and replication $$r\leq 10$$ and $$r(k-1)-(v-1)\lfloor r(k-1)/(v-1)\rfloor \leq 9$$.

MSC:
 62K10 Statistical block designs 62K05 Optimal statistical designs 05B05 Combinatorial aspects of block designs
Software:
DESIGN; GENREG; Mathematica
Full Text:
References:
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