Steiner systems $S(2,6,226)$ and $S(2,6,441)$ exist

TL;DR

This paper reports the discovery of specific Steiner systems using computer search, resolving two previously undecided cases in the classification of such systems.

Contribution

The authors identified new Steiner systems $S(2,6,226)$ and $S(2,6,441)$, advancing the classification of these combinatorial designs.

Findings

Found seven non-isomorphic 1-rotational Steiner systems $S(2,6,226)$

Discovered six point-transitive Steiner systems $S(2,6,441)$

Resolved two of 29 previously undecided cases for $S(2,6,v)$

Abstract

Via computer search, we found seven non-isomorphic $1$-rotational Steiner systems $S(2,6,226)$ and six point-transitive Steiner systems $S(2,6,441)$, resolving two of $29$ previously undecided cases for $S(2,6,v)$.