engleski

On Some Symmetric (45, 12, 3) and (40, 13, 4) Designs

We show that a symmetric (45, 12, 3) design and two symmetric (40, 13, 4) designs can be constructed from the group PSp(4, 3), defining an incidence relation on the conjugacy classes of maximal subgroups. These designs possess symmetric incidence matrices with constant diagonal, which are adjacency matrices of strongly regular graphs. Symplectic group PSp(4, 3) acts transitively on the constructed designs and strongly regular graphs.

Symmetric design; symplectic group; automorphism group; strongly regular graph

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