Simple 3-designs of \(\mathrm{PSL}(2,2^n)\) with block size 6
type: Item
instance of: scholarly article
title: Simple 3-designs of \(\mathrm{PSL}(2,2^n)\) with block size 6
zbMATH Open document ID: 1142.05004
author: Weixia Li
author: Hao Shen
published in: Discrete Mathematics
publication date: 2008-05-29T00:00:00Z
review text: 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 \(0 \leq \lambda \leq \binom{2^n-2}{3}\).
reviewed by: Charles J. Colbourn
Mathematics Subject Classification ID: 05B05
zbMATH DE Number: 5280741
zbMATH Keywords: 3-design
zbMATH Keywords: linear fraction
zbMATH Keywords: projective special linear group
MaRDI profile type: Publication
full work available at URL: j.disc.2007.08.030
OpenAlex ID: W1996184321
cites work: Q3050438
cites work: Large sets of 3‐designs from psl(2, q), with block sizes 4 and 5
cites work: Q3251484
cites work: Q4044675
cites work: Quadruple systems of the projective special linear group PSL(2,q),q ? 1 (mod 4)
cites work: 3-Designs of PSL(2, 2n) With block sizes 4 and 5
cites work: Q3216750
DOI: 10.1016/J.DISC.2007.08.030
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description: scientific article; zbMATH DE number 5280741