A Steiner 5-Design on 36 Points

Authors:
Anton Betten;Reinhard Laue;Alfred Wassermann
Affiliations:
Mathematical Department, University of Bayreuth, D-95440 Bayreuth;Mathematical Department, University of Bayreuth, D-95440 Bayreuth;Mathematical Department, University of Bayreuth, D-95440 Bayreuth
Venue:
Designs, Codes and Cryptography - Special issue on designs and codes—a memorial tribute to Ed Assmus
Year:
1999

Citing 4
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Abstract

Up to now, all known Steiner 5-designsare on q+1 points where q\equiv 3(mod 4) is a prime power and the design is admitting PSL(2,q)as a group of automorphisms. In this article we present a 5-(36,6,1)design admitting PGL(2,17)\times C_2 as a groupof automorphisms. The design is unique with this automorphismgroup and even for the commutator group PSL(2,17)\timesId_2 of this automorphism group there exists no furtherdesign with these parameters. We present the incidence matrixof t-orbits and block orbits.