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arXiv · 1706.05727

On transitive designs and strongly regular graphs constructed from Mathieu group $M_{11}$

Dean Crnkovic·Andrea Svob
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Abstract

In this paper we construct structures from Mathieu group $M_{11}$. We classify transitive $t$-designs with 11, 12 and 22 points admitting a transitive action of Mathieu group $M_{11}$. Thereby we proved the existence of designs with parameters 3-(22,7,18) and found first simple designs with parameters 4-(11,5,6) and 5-(12,6,6). Additionally, we proved the existence of $2$-designs with certain parameters having 55 and 66 points. Furthermore, we classified strongly regular graphs on at most 450 vertices admitting a transitive action of the Mathieu group $M_{11}$.

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Dean Crnkovic, Andrea Svob. 2017-06-18. On transitive designs and strongly regular graphs constructed from Mathieu group $M_{11}$. https://arxiv.org/abs/1706.05727

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