More large sets of resolvable MTS and resolvable DTS with odd orders

AbstractIn this paper, we first give a method to construct large sets of resolvable Mendelsohn triple systems of order q+2, where q=6t+1 is a prime power. Then, using a computer, we find solutions for t∈T={35,38,46,47,48,51,56,60}. Furthermore, by a method we introduced, large sets of resolvable directed triple systems with the same orders are obtained too. Finally, by the tripling construction and product construction for LRMTSs and LRDTSs, and by new results for LR-designs, we obtain the existence of an LRMTS(v) and an LRDTS(v) for all v of the formv=(6t+3)∏m∈M(2·7m+1)∏n∈N(2·13n+1),where t∈T and M and N are finite multisets of non-negative integers. This provides more infinite classes for LRMTSs and LRDTSs with odd orders