Simple \(3\)-Designs of PS \(L(2, 2^n)\) with Block Size \(7\)

Abstract

This paper devotes to the investigation of \(3\)-designs admitting the special projective linear group \(\mathrm{PSL}(2, 2^n)\) as an automorphism, and we determine all the possible values of \(n\) in the simple \(3-(2^n + 1, 7, \lambda)\) designs admitting \(\mathrm{PSL}(2,2^n)\) as an automorphism group.