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New 5-designs with automorphism group PSL(2, 23)

✍ Scribed by Masaaki Kitazume; Akihiro Munemasa

Publisher: John Wiley and Sons
Year: 1999
Tongue: English
Weight: 399 KB
Volume: 7
Category: Article
ISSN: 1063-8539
DOI: 10.1002/(sici)1520-6610(1999)7:2<147::aid-jcd6>3.0.co;2-w

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✦ Synopsis

Blocks of the unique Steiner system S(5, 8, 24) are called octads octads octads. The group PSL(2, 23) acts as an automorphism group of this Steiner system, permuting octads transitively. Inspired by the discovery of a 5-(24, 10, 36) design by Gulliver and Harada, we enumerate all 4and 5-designs whose set of blocks are union of PSL(2, 23)-orbits on 10-subsets containing an octad.

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