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Abstract

Up to now, all known Steiner 5-designs are on q + 1 points where q ≡ 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) × C 2 as a group of automorphisms. The design is unique with this automorphism group and even for the commutator group PSL(2, 17) × Id 2 of this automorphism group there exists no further design with these parameters. We present the incidence matrix of t-orbits and block orbits.

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Betten, A., Laue, R. & Wassermann, A. A Steiner 5-Design on 36 Points. Designs, Codes and Cryptography 17, 181–186 (1999). https://doi.org/10.1023/A:1026427226213

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