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Circular neighbor-balanced designs universally optimal for total effects. (English) Zbl 1121.62070
Summary: In many experiments, the performance of a subject may be affected by some previous treatments applied to it apart from the current treatment. This motivates the studies of the residual effects of the treatments in a block design. This paper shows that a circular block design neighbor balanced at distances up to \(\gamma \leq k - 1\), where \(k\) is the block size, is universally optimal for total effects under the linear models containing the neighbor effects at distances up to \(\gamma\) among the class of all circular binary block designs. Some combinatorial approaches to constructing these circular block designs neighbor-balanced at distances up to \(k - 1\) are provided.

MSC:
62K05 Optimal statistical designs
62K10 Statistical block designs
05B05 Combinatorial aspects of block designs
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