Some construction of group divisible designs GDD(m,n; 1, 3)

Abstract

A group divisible design GDD(m,n; 1,3) is an ordered pair (V, B) where V is an (m + n)-set of symbols and B is a collection of 3-subsets (called blocks) of V satisfying the following properties: the (m + n)-set is divided into two groups of size m and n; each pair of symbols from the same group occurs in exactly one block in B; and each pair of symbols from different groups occurs in exactly three blocks in B. Given positive integers m and n, two necessary conditions on m and n for the existence of a GDD(m,n;1,3) are 6 | [m(m - 1) + n(n - 1)] and m ≢ n(mod 2). We show that these conditions are sufficient for the most cases. © 2015 Academic Publications, Ltd.