Gregarious GDDs with Two Associate Classes

The existence of group divisible designs with two associate classes has been studied for over 50 years. Probably the most difficult cases to solve are those in which the number of groups is less than the size of the blocks. Recently, such an existence problem was solved in the case where the groups have the same size and the blocks have size 3. In this paper, we continue to focus on blocks of size 3, solving the existence problem when the required designs are gregarious (each block intersects each group). These designs are tight to construct in the sense that they satisfy equality in one of the bounds required for GDDs to exist.