GBRDs over groups of orders ≤100 or of order pq with p, q primes

AbstractThere 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 pq where p,q are primes and for groups of all orders ≤100 except possibly 32, 36, 48, 54, 60, 64, 72, 96