Cyclic Designs

Abstract

Cyclic designs are incomplete block designs consisting of sets of blocks where in each set successive blocks are obtained in a cyclic manner from the first block of the set. It is convenient to label the objects (treatments) by the integers 0, 1, …, n-. Then if for a particular set the first block consists of, say, the objects 0, h, i, j, then the second block would contain 1, h+1, i+1, j+1. The remaining blocks in the set are obtained similarly, with reduction modulo n whenever an object label exceeds n-1. A cyclic design consists of such sets or combinations of sets, and will be said to be of size (n, k, r) if the block size is k and the object occurs r times. Cyclic designs are a subclass of partially balanced incomplete block (PBIS) designs. In this dissertation all non-isomorphic designs for combinations of n, k, and r are enumerated, and their efficiencies computed. Non-isomorphic designs are those which are not derivable from any other by a relabeling or permutation of the object labels. A method of analysis is presented which utilizes the cyclic property of the designs. The efficiencies are compared with those of two-associate class PBIB designs and a discussion on the utility of the designs is also given.