engleski

Menon Designs with Parameters (256, 120, 56)

There are exactly 18 symmetric (256, 120, 56) designs admitting an automorphism group isomorphic to $Frob_{; ; 17 \cdot 8}; ; \times Z_3$ acting with orbit size distribution (1, 17, 17, 17, 51, 51, 51, 51) for blocks and points. For sixteen of these designs the full automorphism group has order 408 and is isomorphic to $Frob_{; ; 17 \cdot 8}; ; \times Z_3$, and the remaining two designs have $Frob_{; ; 17 \cdot 8}; ; \times Frob_{; ; 7 \cdot 3}; ; $ as full automorphism group. All 18 designs are self-dual. The derived designs (with respect to the fixed block) of the designs with full automorphism group isomorphic to $Frob_{; ; 17 \cdot 8}; ; \times Frob_{; ; 7 \cdot 3}; ; $ are 1-rotational.

symmetric design; Menon design; Hadamard matrix; automorphism group

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