Simple 3-designs of \(\mathrm{PSL}(2,2^n)\) with block size 6
It is proved that a simple \(3\)-\((2^n+1,6,\lambda)\) design that admits PSL\((2,2^n)\) as an automorphism group exists if and only if (1) \(n \equiv 0 \pmod{4}\), \(\lambda \equiv 0 \pmod{20}\), and \(0 \leq \lambda \leq \binom{2^n-2}{3}-24\); (2) \(n \equiv 0 \pmod{4}\), \(\lambda \equiv 4 \pmod{20}\), and \(0 \leq \lambda \leq \binom{2^n-2}{3}\); or (3) \(n \not\equiv 0 \pmod{4}\), \(\lambda \equiv 0 \pmod{20}\), and \(0 \leq \lambda \leq \binom{2^n-2}{3}\).
scientific article; zbMATH DE number 5280741
scientific article