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 , two Steiner systems , and ten Steiner systems are presented. This resolves two of undecided cases for block designs with block length , and one of cases for block designs with block length , mentioned in Handbook of Combinatorial Designs.
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}
}