GBRDs with Block Size Three over 2-Groups, Semi-Dihedral Groups and Nilpotent Groups - Abel, R. Julian R.; Combe, Diana; Nelson, Adrian M.; Palmer, William D. (The Electronic Journal of Combinatorics, 2011)
There are well known necessary conditions for the existence of a generalized Bhaskar Rao design over a group $\mathbb{G}$, with block size $k=3$. We prove that they are sufficient for nilpotent groups $\mathbb{G}$ of even order, and in particular for $2$-groups. In addition, we prove that they are sufficient for semi-dihedral groups.