English

There exist Steiner systems $S(2,7,505)$, $S(2,7,589)$, and $S(2,8,624)$

Combinatorics 2026-04-14 v3

Abstract

In this note two Steiner systems S(2,7,505)S(2,7,505), two Steiner systems S(2,7,589)S(2,7,589), and ten Steiner systems S(2,8,624)S(2,8,624) are presented. This resolves two of 2121 undecided cases for block designs with block length 77, and one of 3737 cases for block designs with block length 88, mentioned in Handbook of Combinatorial Designs.

Keywords

Cite

@article{arxiv.2604.04975,
  title  = {There exist Steiner systems $S(2,7,505)$, $S(2,7,589)$, and $S(2,8,624)$},
  author = {Ivan Hetman},
  journal= {arXiv preprint arXiv:2604.04975},
  year   = {2026}
}