International Journal of Group Theory (Sep 2019)
Transitive $t$-designs and strongly regular graphs constructed from linear groups $L(2,q)$, $q leq 23$
Abstract
In this paper we construct transitive $t$-designs from the linear groups $L(2,q), q leq 23$. Thereby we classify $t$-designs, $t ge 2$, admitting a transitive action of the linear groups $L(2,q), q leq 23$, up to 35 points and obtained numerous transitive designs, for $36leq vleq 55$. In many cases we proved the existence of $t$-designs with certain parameter sets. Among others we constructed $t$-designs with parameters $2$-$(55,10,4)$, $3$-$(24,11,495)$, $3$-$(24,12, 5m), m in {11, 12,22, 33, 44, 66, 132}$. Furthermore, we constructed strongly regular graphs admitting a transitive action of the linear groups $L(2,q), q leq 23$.
Keywords