Small Steiner 3-designs

This dataset contains the known Steiner 3-(v,k,1) designs with v<=50 and their extensions to Steiner 5-designs. Rotational Steiner quadruple systems of orders v=46 and v=92 are also included, as well as Steiner 2-designs with parameters 2-(40,4,1), 2-(41,5,1), 2-(45,5,1), and 2-(49,4,1). The designs were compiled in the study M. Kiermaier, V. Krčadinac, A. Wassermann, "Steiner 3-designs as extensions", preprint, 2025, https://arxiv.org/abs/2509.23483. The files are gnu-zipped text files containig designs in a format compatible with the computer algebra system GAP and the DESIGN package. Each file named t-v-k-lambda.des.gz contains a list of t-(v,k,lambda) designs. An on-line table of the designs in this dataset is also available here.