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

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.

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

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

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

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

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

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

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AI智能校验