Block-transitive and point-primitive $2$-$(v,k,2)$ designs with sporadic socle

Xiaohong Zhang, Shenglin Zhou

The purpose of this paper is to classify all pairs $(\mathcal{D},G)$, where $\mathcal{D}$ is a non-trivial $2$-$(v,k,2)$ design, and $G\le Aut(\mathcal{D})$ acts transitively o…