GBRDs over groups of orders or of order with , primes

There are well-known necessary conditions for the existence of a generalized Bhaskar Rao design over a group G , with block size k = 3 . It has been conjectured that these necessary conditions are indeed sufficient. We prove that they are sufficient for groups G of order p q where p , q are primes and for groups of all orders ≤ 100 except possibly 32, 36, 48, 54, 60, 64, 72, 96.