Classification of Cyclic Steiner Quadruple Systems.

The problem of classifying cyclic Steiner quadruple systems (CSQSs) is considered. A computational approach shows that the number of isomorphism classes of such designs with orders 26 and 28 is 52,170 and 1,028,387, respectively. It is further shown that CSQSs of order 2 p, where p is a prime, are isomorphic iff they are multiplier equivalent. Moreover, no CSQSs of order less than or equal to 38 are isomorphic but not multiplier equivalent. [ABSTRACT FROM AUTHOR]