Classification of 6-(14,7,4) Designs with Nontrivial Automorphism Groups

摘要

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.