More c-Bhaskar Rao designs with small block size Original Research Article

In this article we resolve some of the open problems left in two other articles. A c-Bhaskar Rao design, i.e., a c-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 c. We complete Greig, Hurd, McCranie and Sarvateʹs work on the spectrum of c-BRD(v,4,λ) when c ≠ 0. In the classic (i.e., c = 0) case, we establish the existence of 0-BRD(3t+1,4,2) for all 3t+1⩾433, with at most 30 smaller exceptions, all with t odd. Morgan, Preece and Rees have given a list of nested BIBDs with v⩽16 and r⩽30; they have one open case. By reformulating this problem, and constructing a (−1)-BRD(16,10,9), we provide a solution for this open case.