Steiner systems S(2,6,121/126), S(2,7,169) based on difference families

Abstract

In this paper new Steiner systems $S(2,6,121)$, $S(2,6,126)$, $S(2,7,169)$ are introduced. Also some non-existence results for line lengths $\mathrm{7..11}$ are presented. There is no solid proof that presented algorithm is exhaustive or correct, but it produces same results on already known difference families for line lengths $\mathrm{3..6}$. Due to calculation-based approach this paper probably won't be published, but will be submitted to arxiv as it contains some new results