We give a complete solution for the existence problem of group divisible designs (or PBIBDs) with blocks of size k = 3, four groups of size (n, n, n, 1), and any two indices (λ1, λ2). Moreover, we introduce a construction of infinitely many group divisible designs with t groups of size n and one group of size 1. The construction technique utilizes our main result, together with some other known...
