GDDs with two associate classes and with one group of size 1 and m groups of size n and λ_1=3, λ_2=1

Abstract

A group divisible design GDD  is an ordered pair   where   is an -set of symbols and  is a collection of 3-subsets (called blocks) of  satisfying the following properties: the -set is divided into 1 group of size 1 and  groups of size ; each pair of symbols from the same group occurs in exactly blocks in ℬ ; and each pair of symbols from different groups occurs in exactly   blocks in ℬ. In this paper we find necessary and sufficient conditions for the existence of a GDD , where .