There are well known necessary conditions for the existence of a generalized Bhaskar Rao design over a group G, with block size k = 3. We prove that they are sufficient for nilpotent groups G of even order, and in particular for 2-groups. In addition, we prove that they are sufficient for semi-dihedral groups.

We introduce, for block size 3, the problem of minimal enclosings of GDDs with u groups of size g into GDDs with u groups of size g + 1. We prove the necessary conditions are sufficient for the embedding of any GDD with group size 1, i.e., a BIBD(v, 3, λ), into a GDD with v groups of size 2. Minimal faithful enclosings of GDDs are given for group size 2 with any index into GDDs with group size ...

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