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.