Classification of 6‐(14,7,4) designs with nontrivial automorphism groups

Abstract

Abstract In this paper, we introduce some intersection matrices for t ‐designs. Utilizing these matrices together with a modified version of a backtracking algorithm, we classify all 6‐(14,7,4) and 5‐(13,6,4) designs with nontrivial automorphism groups and obtain 13 and 21 such designs, respectively. © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 180–194, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ) DOI 10.1002/jcd.10004