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1999•Journal of Combinatorial DesignsRequires access

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

Masaaki Kitazume, Akihiro Munemasa

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Abstract

Blocks of the unique Steiner system S(5, 8, 24) are called 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 4- and 5-designs whose set of blocks are union of PSL(2, 23)-orbits on 10-subsets containing an octad. © 1999 John Wiley & Sons, Inc. J Combin Designs 7: 147–155, 1999

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What this paper is about

Blocks of the unique Steiner system S(5, 8, 24) are called 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 4- and 5-designs whose set of blocks are union of PSL(2, 23)-orbits on 10-subsets containing an octad. © 1999 John Wiley & Sons, Inc. J Combin Designs 7: 147–155, 1999

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Available abstract

Blocks of the unique Steiner system S(5, 8, 24) are called 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 4- and 5-designs whose set of blocks are union of PSL(2, 23)-orbits on 10-subsets containing an octad. © 1999 John Wiley & Sons, Inc. J Combin Designs 7: 147–155, 1999

Key concepts: PSL, Mathematics, Automorphism group, Combinatorics, Group (periodic table), Automorphism, Set (abstract data type), Steiner system

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