Glasnik Matematicki, Vol. 58, No. 2 (2023), 225-232. \( \)

ON SYMMETRIC \(2\)-\((70,24,8)\) DESIGNS WITH AN AUTOMORPHISM OF ORDER \(6\)

Sanja Rukavina and Vladimir D. Tonchev

Faculty of Mathematics, University of Rijeka, 51 000 Rijeka, Croatia
e-mail:sanjar@math.uniri.hr

Department of Mathematical Sciences, Michigan Technological University, Houghton, MI 49931, USA
e-mail:tonchev@mtu.edu

Abstract.   In this paper we analyze possible actions of an automorphism of order six on a \(2\)-\((70, 24, 8)\) design, and give a complete classification for the action of the cyclic group of order six \(G= \langle \rho \rangle \cong Z_6 \cong Z_2 \times Z_3\), where \(\rho^3\) fixes exactly \(14\) points (blocks) and \(\rho^2\) fixes \(4\) points (blocks). Up to isomorphism there are \(3718\) such designs. This result significantly increases the number of previously known \(2\)-\((70,24,8)\) designs.

2020 Mathematics Subject Classification.   05B05, 94B05

Key words and phrases.   Symmetric design, automorphism group

https://doi.org/10.3336/gm.58.2.05

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