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A Blokhuis, L Lovsz, L Storme, T Sz?nyi

On multiple blocking sets in Galois planes

This article continues the study of multiple blocking sets in PG(2, q). In [A. Blokhuis, L. Storme, T. Sz?nyi, Lacunary polynomials, multiple blocking sets and Baer subplanes. J. London Math. Soc. (2) 60 (1999), 321–332. MR1724814 (2000j:05025) Zbl 0940.51007], using lacunary polynomials, it was proven that t-fold blocking sets of PG(2, q), q square, t < q^¼/2, of size smaller than t(q + 1) + c_qq^⅔, with c_q = 2^−⅓ when q is a power of 2 or 3 and c_q = 1 otherwise, contain the union of t pairwise disjoint Baer subplanes when t ≥ 2, or a line or a Baer subplane when t = 1. We now combine the method of lacunary polynomials with the use of algebraic curves to improve the known characterization results on multiple blocking sets and to prove a t (mod p) result on small t-fold blocking sets of PG(2, q = pⁿ), p prime, n ≥ 1.

Advances in Geometry, Walter de Gruyter

Print ISSN: 1615-715X
Volume: 7, 01/2007
Pages: 39 - 53

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