Circular neighbor-balanced designs universally optimal for total effects

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 neighborbalanced at distances up to γ ≤ 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 γ 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. © Science in China Press 2007.