Infinite families of generalized Bhaskar Rao designs

We show that GBRD(p,1/2(p-1), 1/8(p-1)(p-3);EA(1/2p-1)) exist for all prime powers p ≡ 3 (mod 4). We also show that GBRD(p,1/2(p - 1), 1/4(p - 1)(p - 3); EA(1/2(p - 1)) exist for all prime powers p ≡ 1 (mod 4). This allows us to give a new proof that a BIBD(f(ef + 1),(ef + 1)(ef2 + f -1),ef + f -1,f,f - 1) exists whenever p = ef + 1 is a prime power. This gives many new GBRDs including a GBRD(19,9,36;EA(9)), a GBRD(13,6,30;Z6) and a GBRD(17,8,6;EA(8)).