(s, r; μ)-nets and alternating forms graphs

AbstractThe equivalence between Bruck nets and mutually orthogonal latin squares is extended to (s, r; μ)- nets and mutually orthogonal quasi frequency squares. We investigate geometries arising from classical forms such as bilinear forms, alternating bilinear forms, hermitian forms and symmetric forms and show that (s, r; μ)-nets provide the right building blocks for each of these geometries with suitable values of μ. Toward the goal of geometric classification of distance-regular graphs, the local structure of the case of alternating forms graphs is stressed