The existence spectrum for large sets of pure Hybrid triple systems

An LPHTS(v)LPHTS(v) is a collection of 4(v−2)4(v−2) disjoint pure Hybrid triple systems on the same set of vv elements. In Fan (2010), it is showed that there exists an LPHTS(v)LPHTS(v) for v≡0,4v≡0,4 mod 6. In this paper, we establish the existence of an LPHTS(v)LPHTS(v) for v≡1,3v≡1,3 mod 6, v>3v>3. Finally, the spectrum for LPHTSsLPHTSs is completely determined.