In this note, a construction of the large sets of pairwise disjoint Mendelsohn triple systems of order 72k + 6, where k > 1 and k F 1 or 2 (mod 3), is given.
Let X be a set of v elements (v 2 3). A cyclic triple from X is a collection of three pairs (x, y), (y,z) and (z, x), where x,y and z are distinct elements of X. The cyclic triple is denoted by (x, y, z) or ( y, z, x) or (z, x, y). A Mendelsohn triple system on X is a pair (X, B) where B is a collection of cyclic triples from X such that each ordered pair of distinct elements of X is covered by a unique cyclic triple from B. The system on
X( [XI= v) is denoted by MTS(v). Mendelsohn
[l] proved that the spectrum for MTS(u)s is the set of all v-0 or 1 (mod 3) and v#6.
A large set of pairwise disjoint MTS(v)s is a collection of u-2 pairwise disjoint MTS(v)s. It is denoted by LMTS(o). Up to now, all known results about LMTS(v) are: (Rl) There exists an LMTS(u) for v-1,3 (mod 6) [2]; (R2) If there exists an LMTS(v), then there exists an LMTS(3n) [3]; (R3) If there exists an LMTS(V+ 1) and v>,3, then there exists an LMTS(~V+ 1) [3];
(R4) For p-1 or 5 (mod 6), if there exists an LMTS(q +2), then there exists an LMTS(pq + 2) C2,41;