Overlarge sets of Mendelsohn triple systems with resolvability

An OLRMTS(v) (OLARMTS(v)) over a (v+1)(v+1)-set XX is a collection {(X∖{x},Bx):x∈X}{(X∖{x},Bx):x∈X} of v+1v+1 pairwise disjoint resolvable (almost resolvable) Mendelsohn triple systems of order vv. In this paper several direct construction methods for OLRMTSs and OLARMTSs are presented and then applied to produce some new orders; the smallest unknown OLRMTS(v) for v=18,24v=18,24, the smallest unknown OLARMTS(v) for v=19,22,28,31v=19,22,28,31, and some other small designs are displayed; a few new existence families are also obtained by known recursive constructions.