Abstract
Aspread inPG(n, q) is a set of lines which partitions the point set. A packing inPG(n, q) (n odd) is a partition of the lines into spreads. Two packings ofPG(n, q) are calledorthogonal if and only if any two spreads, one from each packing, have at most one line in common. Recently, R. D. Baker has shown the existence of a pair of orthogonal packings inPG(5, 2). In this paper we enumerate all packings inPG(5, 2) having both an automorphism of order 31 and the Frobenius automorphism. We find all pairs of orthogonal packings of the above type and display a set of six mutually orthogonal packings. Previously the largest set of orthogonal packings known inPG(5, 2) was two.
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Stinson, D.R., Vanstone, S.A. Orthogonal packings inPG(5, 2). Aeq. Math. 31, 159–168 (1986). https://doi.org/10.1007/BF02188184
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DOI: https://doi.org/10.1007/BF02188184