Enumeration of t-Designs Through Intersection Matrices

Abstract

In this paper, we exploit some intersection matrices to empower a backtracking approach based on Kramer–Mesner matrices. As an application, we consider the interesting family of simple t-(t + 8,t + 2,4) designs, 1 ≤ t ≤ 4, and provide a complete classification for t e 1,4, as well as a classification of all non-rigid designs for t e 2,3. We also enumerate all rigid designs for t e 2. The computations confirm the results obtained in Denny and Mathon l4r through the new approach which is much simpler. Finally a list of other designs constructed by this method is provided.