Higher Associate Cyclical Association Scheme and Orthogonal Factorial Structure

Abstract

Cotter, John and Smith (1973) proposed a class of inter-effect orthogonal designs which we shall refer to as Ω-structure. We have established that a necessary and sufficient condition for a block design to have Ω-structure is that the levels of first (n-1) factors give a block design having higher associate cyclic association scheme. while the block design given by the levels of the n-th factor satisfy K-structure [ Mukherjee (1979)] for single-factor experiment. Structure of the design when all the n factors give a block design having higher associate cyclical association scheme has also been discussed. We have further identified higher associate cyclic partially balanced incomplete block designs as a class of block designs having orthogonal factorial strueture.