Case studies and new results in combinatorial enumeration

Abstract

A 1976 block design enumeration algorithm has been reimplemented with a number of enhancements. Its use is demonstrated with a number of case studies involving different kinds of incidence structures. New results include the enumeration of weakly union-free twofold triple systems of orders 12 and 13, Mendelsohn triple systems of orders 10 and 12, 2-(8, 4, 9), 2-(10, 4, 4), 2-(16, 4, 2), 3-(11, 5, 4) and 4-(12, 6, 4) block designs, and 2-(7, 3, λ) designs for 14 ≤ λ ≤ 16. Some of these results correct enumerations previously published in the literature. Additional results confirm independently produced results, some of which have been published quite recently. © 2000 John Wiley & Sons, Inc. J Combin Designs 8: 239–260, 2000