Abstract. A hypergraph is 3-uniform if every edge contains exactly 3 vertices. Further, a hypergraph is 2-subset-regular if there exists t, also called the 2-valence, such that each 2-element subset is a subset of exactly t edges. Finally, a hypergraph is self-complementary if it is isomorphic to its complement.

We show that a 2-subset-regular self-complementary 3-uniform hypergraph with n vertices exists if and only if n is congruent to 2 modulo 4.