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On the minimum size of complete arcs and minimal saturating sets in projective planes

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Abstract

The minimum size of a complete arc in the planes PG(2, 31) and PG(2, 32) and of a 1-saturating set in PG(2, 17) and PG(2, 19) is determined. Also, the minimal 1-saturating sets in PG(2, 9) and PG(2, 11) are classified. In addition, the minimal 1-saturating sets of the smallest size in PG(2, q) are classified for 16 ≤ q ≤ 23. These results have been found using a computer-based exhaustive search that exploits projective equivalence properties.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Via Vanvitelli 1, Perugia, 06123, Italy

    Daniele Bartoli, Giorgio Faina, Stefano Marcugini & Fernanda Pambianco

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  1. Daniele Bartoli
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  2. Giorgio Faina
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  3. Stefano Marcugini
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  4. Fernanda Pambianco
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Correspondence to Giorgio Faina.

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Bartoli, D., Faina, G., Marcugini, S. et al. On the minimum size of complete arcs and minimal saturating sets in projective planes. J. Geom. 104, 409–419 (2013). https://doi.org/10.1007/s00022-013-0178-y

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