Group Divisible Design (4, n, n + 1, 4; λ1, λ2), for n ≥ 4

Abstract

This work is about Group Divisible Designs (GDDs) of block size four on three groups of different sizes n1 = 4, n2 = n and n3 = n + 1 where n ≥ 4. We first establish necessary conditions for the existence of the GDD using relationships between the parameters of the GDD and then prove that these conditions are sufficient for several families of GDDs.