Some rigid Steiner 5‐designs

Hitherto, all known non-trivial Steiner systems S$(5,k,v)$ have, as a group of automorphisms, either PSL$(2,v-1)$ or PGL$(2,\frac{v-2}{2})\times C_2$. In this paper, systems S$(5,6,72)$, S$(5,6,84)$ and S$(5,6,108)$ are constructed that have only the trivial automorphism group.