The existence of augmented resolvable Steiner quadruple systems

An augmented Steiner quadruple system of order v is an ordered triple (X,B,E), where (X,B) is an SQS(v) and E is the set of all 2-subsets of X. An augmented Steiner quadruple system (X,B,E) of order v is resolvable if B@?E can be partitioned into n=(v-1)(v+4)/6 parts B@?E=P"1|P"2|...|P"n such that each part P"i is a partition of X. 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] conjectured that there exists a resolvable augmented Steiner quadruple systems of order v for any positive integer v=2 or 10 (mod 12). In this paper, we show that the Hartman and Phelps conjecture is true.