Constructions of dihedral Steiner quadruple systems

A dihedral SQS is an SQS admitting a point-regular dihedral automorphism group. Some constructions of dihedral SQSs are established in this paper. We also prove that for v≡2,4(mod6), there is a dihedral SQS(v) if there is a dihedral H(p,2,4,3) design or an S-cyclic SQS(2p) for each odd prime divisor p of v. As a corollary, we enlarge the set of known values of v for which there exists a dihedral SQS(v).