Enumeration of t-Designs Through Intersection Matrices

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-ðtþ 8; tþ 2; 4Þ designs, 1 t 4, and provide a complete classification for t 1⁄4 1; 4, as well as a classification of all non-rigid designs for t 1⁄4 2; 3. We also enumerate all rigid designs for t 1⁄4 2. The computations confirm the results obtained in Denny and Mathon [4] through the new approach which is much simpler. Finally a list of other designs constructed by this method is provided.