The existence of resolvable Steiner quadruple systems
A Steiner quadruple system of order \(\nu\) is a set X of cardinality \(\nu\), and a set Q, of 4-subsets of X, called blocks, with the property that every 3-subset of X is contained in a unique block. A Steiner quadruple system is resolvable if Q can be partitioned into parallel classes (partitions of X). A necessary condition for the existence of a resolvable Steiner quadruple system is that \(\nu\) \(\equiv 4\) or 8 (mod 12). In this paper we show that this condition is also sufficient for all values of \(\nu\), with 24 possible exceptions.
scientific article; zbMATH DE number 4083635
scientific article