A family of $t$-regular self-complementary $k$-hypergraphs

Abstract

We use the recursive method of construction large sets of t-designs given by Qiu-rong Wu (A note on extending t-designs‎, ‎{em Australas‎. ‎J‎. ‎Combin.}‎, ‎{bf 4} (1991) 229--235.), and present a similar method for constructing $t$-subset-regular‎ ‎self-complementary $k$-uniform hypergraphs of order $v$‎. ‎As an‎ ‎application we show the existence of a new family of 2-subset-regular‎ ‎self-complementary 4-uniform hypergraphs with $v=16m+3$‎.