We show that GBRD(p, 1/2(p - 1), 1/8(p - 1)(p - 3); EA(1/2(p - 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)(ef~2 + 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; Z_6) and a GBRD(17, 8, 56; EA(8)).
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