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Block designs and strongly regular graphs admitting a transitive action of the Mathieu group M11

In this paper we construct transitive t-designs, for t >= 2, and strongly regular graphs from the Mathieu group M-11. We classify transitive t-designs with 11, 12 and 22 points admitting a transitive action of Mathieu group M-11. The most important result of this classification is proving the existence of a 3-design with parameters 3-(22, 7, 18). Additionally, we prove the existence of 2-designs with certain parameters having 55 and 66 points. Furthermore, we classify strongly regular graphs on at most 450 vertices admitting a transitive action of the Mathieu group M-11.

t-design ; strongly regular graph ; Mathieu group ; transitive group

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