Group Divisible Design (n1, n2, n3,4; λ1, λ2), for n1 = 3,n2 = n and n3 = n + 1

Abstract

The work in this article is about Group Divisible Designs (GDDs) with three groups of sizes n1, n2 and n3, where n1=3, n2=n and n3=n+1 and block size four. First, we establish necessary conditions for the existence of GDD(3,n,n + 1,4;λ1,λ2): for n1=3,n2=n and n3=n+1. Necessary conditions include an inequality .Then we prove that these conditions are sufficient for several families of GDDs. We give an example where parameters satisfy all the necessary conditions including the inequality but the GDD does not exist.