McAloon et al. report being unable to solve the 15 team problem with integer linear programming using CPLEX.
Regin has developed a CP model, for ILOG’s OPL tool that can solve up to 30 team problems.
More recently, he has added a heuristic based on Euler’s theorem for Latin squares to solve 40 team problems in approximately 6 hours.
Hamiez and Hao report solving up to 40 team problems using local search with a tabu restriction.
A more recent paper by the same authors in Discrete Applied Mathemetics solves very large problems with $(T-1) mod 3 = 1$ or $2$ where $T$ is the number of teams using a repair based method.