The spectrum of dihedral quadruple systems

Abstract

An ordered analogue of quadruple systems QS(v, λ)s is dihedral quadruple systems (DQS). A DQS(v, λ) is a pair (S,T) where S is a finite set and T is a family of dihedral quadruples of elements of S called blocks, such that every ordered triple of distinct elements of S belongs to exactly A blocks of T. When λ = 1, Stojakovic solved the spectrum problem of DQS(v, 1). It is proved that a DQS(u, λ) exists if and only if λv(v -l)(v-2) = 0 (mod 8).