Bhaskar Rao designs with block size four

A Bhaskar Rao design, i.e., a BRD(v,k,λ), is formed by signing the v by b incidence matrix of a BIBD(v,k,λ) so that the inner product of any two distinct rows is 0. It is proved in the literature that such designs exist for k=4 with 28 possible exceptions. In this paper, we show that a BRD is equivalent to a special kind of group divisible design (GDD). By using the knowledge of GDDs, we resolve the open cases of BRD(v,4,λ) and complete the spectrum problem on their existence.