Large sets of resolvable Mendelsohn triple systems of prime power sizes

A large set of Mendelsohn triple systems of order v is a partition of all cyclic triples on a v-element set into pairwise disjoint Mendelsohn triple systems of order v. This note addresses questions related to the construction of large sets of Mendelsohn triple systems with resolvable property (each block set having a partition into parallel classes). An improved recursive method is established and a number of new infinite series large sets of prime power sizes are settled by recursion, in combination with already known small cases. To be specific, for all prime powers q<400 and q≡1(mod 3), large sets of resolvable Mendelsohn triple systems of order qn+2 are proved to exist for any positive integer n, possibly except for q=379,397.