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

Abstract

Until now, all known simple \(t-(v, k, \lambda)\) designs with \(t \geq 6\) have \(\lambda \geq 4\). 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 \(\lambda \leq 5\).