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A class of ((p n−p m)(p n−1), p n−p m)-arcs in PG(2, p n)

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Abstract

A (k, d)-arc in PG(2, q) is a set of k points such that some d, but no d+1, of them are collinear. An outstanding problem is to find the maximum value of k for which a (k, d)-arc exists. A construction is given for a class of (k, p n−p m)-arcs in PG(2, p n). These arcs constitute a lower bound on the maximum possible value of k, and a subset of them is shown to be optimal.

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  1. GEC Research Laboratories, Hirst Research Centre, East Lane, HA9 7PP, Wembley, Middlesex, England

    J. R. M. Mason

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  1. J. R. M. Mason
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Mason, J.R.M. A class of ((p n−p m)(p n−1), p n−p m)-arcs in PG(2, p n). Geom Dedicata 15, 355–361 (1984). https://doi.org/10.1007/BF00211704

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  • DOI: https://doi.org/10.1007/BF00211704

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