. 2010, 28(14): 67-69.
There are two kinds of oriented triples on X: the cyclic triple and the transitive triple. A cyclic triple on X is a set of three ordered pairs (x, y), (y, z) and (z, x) of X, which is denoted by <x, y, z> (or <y, z, x>, or <z, x, y>), and a transitive triple on X is a set of three ordered pairs (x, y), (y, z) and (x, z) of X, which is denoted by (x, y, z). An oriented triple system of order v with index λ is a pair (X, B)where X is a v-set and B is a collection of oriented triples on X, called blocks, such that every ordered pair of X belongs to exactly λ blocks of B. If B consists of transitive (or cyclic) triples only, the system is called a directed triple system (or Mendelsohn triple system） of order v with index λ and denoted by DTS(v, λ) (or MTS(v, λ)). If B contains both cyclic triples and transitive triples, the system is called a hybrid triple system of order v with index λ and denoted by HTS(v, λ). A triple system is called simple if there are no repeated blocks in B. A simple DTS(v, λ) is called pure and denoted by PDTS(v, λ) if (x, y, z)∈B implies (z, y, x), (z, x, y), (y, x, z), (y, z, x), (x, z, y)?埸B. A large set of disjoint PDTS(v, λ)s, denoted by LPDTS(v, λ), is a collection of {(X,Bi）}i where each (X,Bi) is a PDTS(v, λ) and ∪iBi is a partition of all transitive triples on X. In this paper, a tripling construction for LPDTS(v, 3) is presented, and one infinite family for the existence of LPDTS(v, 3) is obtained: for any positive integers v, v≡8,14(mod18）, there exists an LPDTS(v, 3).
