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

Abstract

In this note two Steiner systems $S(2,7,505)$ and two Steiner systems $S(2,7,589)$ are presented. This resolves two of $21$ undecided cases for block designs with block length $7$, mentioned in Handbook of Combinatorial Designs.