Automorphism groups of designs with $\lambda =1$

Abstract

If $G$ is a finite group and $k=q>2$ or $k=q+1$ for a prime power $q$ then, for infinitely many integers $v$, there is a $2$-$(v,k,1)$-design $\mathbf{D}$ for which $\mathrm{Aut}\mathbf{D}\cong G$.