GBRDs over groups of orders ≤100≤100 or of order pqpq with pp, qq primes

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