engleski

Symmetric Designs with Parameters (69, 17, 4) and F39 as a Group of Automorphisms

According to Mathon and Rosa /The CRC Handbook of combinatorial designs, CRC Press, 1996/ there is only one known symmetric design with parameters (69, 17, 4). This known design is given in Beth, Jungnickel, and Lenz /Design theory, B.I. Mannheim, 1985/ ; the Frobenius group F39 of order 39 acts on this design, where Z13 has exactly 4 fixed points and Z3 has exactly 9 fixed points. The purpose of this article is to investigate the converse of this fact with the hope of obtaining in this way at least one more design with these parameters. In fact we obtain exactly one new such design. In this article we have classified all such designs invariant under F39.

Symmetric Design; Frobenius Group; Automorphism Group

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