The existence of regular self-complementary 3-uniform hypergraphs

A k -uniform hypergraph with vertex set V and edge set E is called t -subset-regular if every t -element subset of V lies in the same number of elements of E . In this paper we show that a 1-subset-regular self-complementary 3-uniform hypergraph with n vertices exists if and only if n ≥ 5 and n is congruent to 1 or 2 modulo 4.