Group Divisible Designs with Two Association Classes

Abstract

We investigate group divisible designs with two association classes (known as GDDS, GADs or PBIBDs) with block size 3 and unequal size groups. We completely determine the necessary and sufficient conditions for groups with size vector $(n,1)$ for any $n\ge 3$, and $(n,2,1)$ for $n\in \{2,3,\dots ,6\}$. We also have some general results for $(n_1,n_2,n_3)$.