Block-transitive $3$-$(v,k,1)$ designs on exceptional groups of Lie type

Ting Lan, Weijun Liu, Fu-Gang Yin

Let $\mathcal{D}$ be a non-trivial $G$-block-transitive $3$-$(v,k,1)$ design, where $T\le G\le \mathrm{Aut}(T)$ for some finite non-abelian simple group $T$. It is proved that i…