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Simple 7-designs with small parameters

1999; Wiley; Volume: 7; Issue: 2 Linguagem: Inglês

10.1002/(sici)1520-6610(1999)7

1520-6610

Anton Betten, Reinhard Laue, Alfred Wassermann,

Finite Group Theory Research

Journal of Combinatorial DesignsVolume 7, Issue 2 p. 79-94 Research Article Simple 7-designs with small parameters Anton Betten, Corresponding Author Anton Betten [email protected] Department of Mathematics, University of Bayreuth, D-95440 Bayreuth, Ger˜manyDepartment of Mathematics, University of Bayreuth, D-95440 Bayreuth, Ger˜manySearch for more papers by this authorReinhard Laue, Reinhard Laue Department of Mathematics, University of Bayreuth, D-95440 Bayreuth, Ger˜manySearch for more papers by this authorAlfred Wassermann, Alfred Wassermann Department of Mathematics, University of Bayreuth, D-95440 Bayreuth, Ger˜manySearch for more papers by this author Anton Betten, Corresponding Author Anton Betten [email protected] Department of Mathematics, University of Bayreuth, D-95440 Bayreuth, Ger˜manyDepartment of Mathematics, University of Bayreuth, D-95440 Bayreuth, Ger˜manySearch for more papers by this authorReinhard Laue, Reinhard Laue Department of Mathematics, University of Bayreuth, D-95440 Bayreuth, Ger˜manySearch for more papers by this authorAlfred Wassermann, Alfred Wassermann Department of Mathematics, University of Bayreuth, D-95440 Bayreuth, Ger˜manySearch for more papers by this author First published: 26 March 1999 https://doi.org/10.1002/(SICI)1520-6610(1999)7:2 3.0.CO;2-DCitations: 11AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat Abstract We describe a computer search for the construction of simple designs with prescribed automorphism groups. Using our program package DISCRETA this search yields designs with parameter sets 7-(33, 8, 10), 7-(27, 9, 60), 7-(26, 9, λ) for λ = 54, 63, 81, 7-(26, 8, 6), 7-(25, 9, λ) for λ = 45, 54, 72, 7-(24, 9, λ) for λ = 40, 48, 64, 7-(24, 8, λ) for λ = 4, 5, 6, 7, 8, 6-(25, 8, λ) for λ = 36, 45, 54, 63, 72, 81, 6-(24, 8, λ) for λ = 36, 45, 54, 63, 72, 5-(19, 6, 4), and 5-(19, 6, 6). In several of these cases we are able to determine the exact number of isomorphism types of designs with that prescribed automorphism group. © 1999 John Wiley & Sons, Inc. J Combin Designs 7: 79–94, 1999 REFERENCES 1 M. R. C. M. Berkelaar, lp-solve, a public domain MILP solver, freely available from ftp://ftp.es.ele.tue.nl/pub/lp―solve/. Google Scholar 2 T. Beth, D. Jungnickel, and H. 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