A short note on 3-GDDS with 3 groups and block size 4

Abstract

Necessary conditions for the existence of a \( 3 \)-GDD\((n, 3, k; \lambda_1, \lambda_2)\) are obtained along with some non-existence results. We also prove that these necessary conditions are sufficient for the existence of a \( 3 \)-GDD\((n, 3, 4; \lambda_1, \lambda_2)\) for \( n \) even.