The existence of regular self-complementary 3-uniform hypergraphs

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