Group divisible designs with two groups and three associate classes

Abstract

A group diuisible design GDD (m,n; λ₁, λ₁ꞌ, λ₂) is a 3-tuple (M,N,B) where M and N are disjoint sets of sizes m and n, respectively (called groups), and B is a collection of 3- subsets of M U N (called blocks) such that each pair of elements in M occurs together in exactly λ₁ blocks; each pair of elements in N occurs together in exactly λ₁ꞌ blocks; and each pair of elements from different groups occurs together in exactly λ₂ blocks. In this thesis, we establish a complete solution for the existence problem of such GDDs where m  2, n  2, λ₁  λ₂ and λ₁ꞌ  λ₂.