Simple 3-designs of PSL(2,2ⁿ) with block size 13

2025/03/20 by Kondo, Takara, Nogata, Yuto
#05B05(Primary) #20G40(Secondary) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.16050

Abstract

This paper investigates simple 3-(2ⁿ+1,13,λ) designs admitting PSL(2,2ⁿ) as an automorphism group. We determine all possible values of λ by systematically analyzing the orbits of 13-element subsets under the action of PSL(2, 2ⁿ) on the projective line. While previous research has explored this topic by analyzing the structure of k-element subsets B directly, we approach the problem using group theory and the Cauchy-Frobenius-Burnside lemma. This method provides an efficient framework that can be applied to larger block sizes where traditional enumeration methods become computationally infeasible.

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