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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
##### Keywords:
block design; circular; neighbor-balanced; total effect
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##### References:
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