Abstract
The combinatorial properties of subsquares in orthogonal latin squares are examined. Using these properties it is shown that in appropriate orthogonal latin squares of orderm h blocks of subsquares of orderm h(i−1)/i , wherei dividesh, form the hyperplanes of the affine geometryAG (2i, m h/i ). This means that a given set of mutually orthogonal latin squares may be equivalent simultaneously to a number of different geometries depending on the order of the subsquares used to form the hyperplanes. In the case thati=1, the subsquares become points, the hyperplanes become lines, and the equivalence reduces to the well known result of Bose relating orthogonal latin squares and affine planes.
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