Large sets of pure directed triple systems with index λ

A directed triple system of order v with index λ, briefly by DTS(v, λ), is a pair (X, B) where X is a v-set and B is a collection of transitive triples (blocks) on X such that every ordered pair of X belongs to λ blocks of B. A simple DTS(v, λ) is a DTS(v, λ) without repeated blocks. 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) ∉ B. A large set of disjoint PDTS(v, λ), denoted by LPDTS(v, λ), is a collection of 3(v−2)/λ disjoint pure directed triple systems on X. In this paper, some results about the existence for LPDTS(v, λ) are presented. Especially, we determine the spectrum of LPDTS(v, 2).