Original scientific paper

Some new Menon designs with parameters (196,91,42)

D. Crnković

Abstract

There are exactly 54 symmetric (196,91,42) designs admitting an
automorphism group isomorphic to $Frob_{13 \cdot 6} \times Z_3$ acting with orbit size distribution (1,13,13,13,39,39,39,39) for
blocks and points. For 50 of these designs the full automorphism group
has order 234 and is isomorphic to $Frob_{13 \cdot 6} \times Z_3$.
The remaining four designs have $Frob_{13 \cdot 6} \times Frob_{7 \cdot 3}$ as a full automorphism group.Among these designs there are 18 self-dual designs and 18 pairs of mutually dual ones.
The derived designs (with respect to the fixed block) of the four designs with a full automorphism group of order 1638 are cyclic.

Keywords

symmetric design; Menon design; Hadamard matrix; automorphism group

Hrčak ID:

647

URI

https://hrcak.srce.hr/647

Publication date:

27.12.2005.

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