There exist Steiner systems $S(2,7,505)$, $S(2,7,589)$, and $S(2,8,624)$

Abstract

In this note two Steiner systems $S(2,7,505)$, two Steiner systems $S(2,7,589)$, and ten Steiner systems $S(2,8,624)$ are presented. This resolves two of $21$ undecided cases for block designs with block length $7$, and one of $37$ cases for block designs with block length $8$, mentioned in Handbook of Combinatorial Designs.