THE EXISTENCE OF DOUBLY RESOLVABLE (V,3,2)-BIBDS

A Kirkman square with index lambda, latinicity mu, block size k, and u psilon points, a KSk(upsilon; mu, lambda), is a t x t array (t = lambd a(upsilon - 1)/mu(k - 1)) defined on a upsilon-set V such that (1) eve ry point of V is contained in precisely mu cells of each row and colum n, (2) each cell of the array is either empty or contains a k-subset o f V, and (3) the collection of blocks obtained from the non-empty cell s of the array is a (upsilon, k, lambda)-BIBD. For mu = 1, the existen ce of a KSk(upsilon; mu, lambda) is equivalent to the existence of a d oubly resolvable (upsilon, k, lambda)-BIBD. The spectnun of KS2(upsilo n; 1, 1) or Room squares was completed by Mullin and Wallis in 1975. I n this paper, we determine the spectrum of KS3(upsilon; 1, 2) or DR(up silon, 3, 2)-BIBDs with at present six possible exceptions for upsilon . (C) 1995 Academic Press, Inc.