Bose's Method of Differences Applied to Construct Bhaskar Rao Designs

In this paper we show that BIBD(v, b, r, k, λ), where v = pq or pq + 1, when written in the notation of Bose's method of differences may often be used to find generalized Bhaskar Rao designs GBRD(p, b', r', k, λ; G) where G is a group of order q and vice versa. This gives many new GBRDs including a GBRD(9, 5, 5; Z5) and a GBRD(13, 7, 7; Z7).