3-Designs from PSL(2,q) with cyclic starter blocks

2025/02/18 by Akihide Hanaki, Hanaki, Akihide, Kenji Kobayashi +3
Engineering · #05B05 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2502.13331

openalex publication_date 2025/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider when the projective special linear group over a finite field defines a 3-design with a cyclic starter block. We will show that the equivalences of the existence of such 3-(q+1,5,3) and 3-(q+1,10,18) designs for a prime power q≡ 1\pmod20, and 3-(q+1,13,33) and 3-(q+1,26,150) designs for a prime power q≡ 1\pmod52, respectively.

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