Construction of Optimal Balanced Incomplete Block Designs for Correlated Observations

Abstract

Some methods for the construction of equineighbored balanced incomplete block designs introduced by Kiefer and Wynn (1981) are presented. An algorithm for constructing designs with $k = 3$ is developed. Kiefer and Wynn's result for $k = 3$ is difficult to implement in practice. Our algorithm provides a practical solution and makes use of the decomposition of complete graphs into disjoint Hamiltonian cycles. The construction of designs with $k = v - 1$ and $v - 2$ is also completely solved. The neighbor designs proposed for use in serology are useful for the construction of equineighbored balanced incomplete block designs. Several infinite families of equineighbored balanced incomplete block designs are listed.