A Family of Group Divisible Designs of Block Size Four and Three Groups With \(\lambda_1=2\) and \(\lambda_2=1\) Using MOLS

Abstract

We give a construction for a new family of Group Divisible Designs \((6s + 2, 3, 4; 2, 1)\) using Mutually Orthogonal Latin Squares for all positive integers \(s\). Consequently, we have proved that the necessary conditions are sufficient for the existence of GDD’s of block size four with three groups, \(\lambda_1 = 2\) and \(\lambda_2 = 1\).