3-Group Divisible Designs with 3 Groups and Block Size 5

Abstract

A 3-GDD (n, 2, k, λ1, λ2) was defined by combining the definitions of a group divisible design and a t-design. In this paper, we extend the definitions to 3 groups and block size 5, and we denote such GDD by 3-GDD (n, 3, 5, μ1, μ2). Some necessary conditions for the existence of these GDDs are developed, and several new constructions and specific instances of nonexistence are given.