3- GDDs with 4 Groups and Block Size 5

Abstract

This paper studies a special case of group divisible designs (GDDs) called 3-GDDs, which were defined by extending the definitions of a group divisible designs and a t-design. In particular, the paper looks at a 3-GDD(n, 4, 5; μ₁, μ₂) with 4 groups and block size 5. Necessary conditions for the existence of such GDDs are developed, the non-existence of a 3-GDD(n, 4, 5; μ₁, 0) is proved and several specific instances of non-existence are   given.