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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 q n + 2 are proved to exist for any positive integer n , possibly except for q = 379 , 397 . |
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