On Flag-Transitive $6-(v,k,\lambda )$ Designs with $\lambda \le 5$

Abstract

Until now, all known simple $t-(v,k,\lambda )$ designs with $t\ge 6$ have $\lambda \ge 4$. On the other hand, P. J. Cameron and C. E. Praeger showed that there are no flag-transitive simple $7-(v,k,\lambda )$ designs. In the present paper, we considered the flag-transitive simple $6-(v,k,\lambda )$ designs and proved that there are no non-trivial flag-transitive simple $6-(v,k,\lambda )$ designs with $\lambda \le 5$.