New Steiner systems $S(2,6,v)$ with block length 6

Abstract

In this paper various Steiner systems $S(2,k,v)$ for $k=6$ are collected and enumerated for specific constructions. In particular, two earlier unknown types of $1$-rotational designs are found for the groups $SL(2,5)$ and $(({\mathbb{Z}}_3\times {\mathbb{Z}}_3)⋊{\mathbb{Z}}_3)\times {\mathbb{Z}}_5$. Also new Steiner systems $S(2,6,96),S(2,6,106),S(2,6,111)$ are listed.

24 pages