Resolvable Mendelsohn triple systems with equal sized holes

An HMTS of type {n₁, n₂, ⋖, n_h} is a directed graph which can be decomposed into 3-circuits. If the 3-circuits can be partitioned into parallel classes, then the HMTS is called an RHMTS. In this article it is shown that the RHMTSs of type m^h exist when mh &equiv 0 (mod 3) and (m, h) &ne (1, 6), with the possible exception of h = 6 and , where M₁₇ = {m|m is divisible by a prime less than 17}. The existence of Mendelsohn frames, which is closely related to RHMTS, is also considered in this article. It is proved that a Mendelsohn frame of type t^u exists if and only if u ≥ 4 and t(u - 1) ≡ 0(mod 3) with 2 possible exceptions. © 1997 John Wiley & Sons, Inc. J Combin Designs 5:329–340, 1997