Non-Existence of Point-transitive 2-(106, 6, 1) Designs

Abstract

Let $\mathcal{S}$ be a  linear space with 106 points,  with lines of  size 6,  and let $G$ be an automorphism group of $\mathcal{S}$.  We prove that $G$ cannot be point-transitive. In other words, there exists no point-transitive 2-(106, 6, 1) designs.