The last twenty orders of (1, 2)-resolvable Steiner quadruple systems

A Steiner quadruple system (X, B) is said to be (1, 2)-resolvable if its blocks can be partitioned into r parts such that each point of X occurs in exactly two blocks in each part. The necessary condition for the existence of (1, 2)-resolvable Steiner quadruple systems RSQS(1, 2, v)s is v ≡ 2 or 10 (mod 12). Hartman and Phelps in [A. Hartman, K.T. Phelps, Steiner quadruple systems, in: J.H. Dinitz, D.R. Stinson (Eds.), Contemporary Design Theory, Wiley, New York, 1992, pp. 205–240] posed a question whether the necessary condition for the existence of (1, 2)-resolvable Steiner quadruple systems is sufficient. In this paper, we consider the last twenty orders of (1, 2)-resolvable Steiner quadruple systems and show that the necessary condition for the existence of (1, 2)-resolvable Steiner quadruple systems is also sufficient except for the order 10. © 2012 Elsevier B.V. All rights reserved.