New large sets of resolvable Mendelsohn triple systems

An LRMTS(v)(v) is a large set consisting of v−2v−2 pairwise disjoint resolvable Mendelsohn triple systems defined over the same vv-element set. In this paper a new product construction for LRMTS is displayed by using generalized LR-designs. As well, several new existence families of LRMTS are constructed via 3-wise balanced designs. Finally the existence result of LRMTS is expanded by combining all the known constructions.