The spectrum for large sets of pure directed triple systems.

An LPDTS( ν) is a collection of 3( ν − 2) disjoint pure directed triple systems on the same set of ν elements. It is showed in Tian’s doctoral thesis that there exists an LPDTS( gn) for gn ≡ 0,4 (mod 6), ν ⩾ 4. In this paper, we establish the existence of an LPDTS( ν) for ν ≡ 1,3 (mod 6), ν > 3. Thus the spectrum for LPDTS( ν) is completely determined to be the set { ν:ν ≡ 0, 1 (mod 3), ν ⩾ 4}. [ABSTRACT FROM AUTHOR]