منابع مشابه
Largest Minimal Blocking Sets in PG(2,8)
Bruen and Thas proved that the size of a large minimal blocking set is bounded by q ffiffiffi q p þ 1. Hence, if q 1⁄4 8, then the maximal possible size is 23. Since 8 is not a square, it was conjectured that a minimal blocking 23-set does not exist in PGð2; 8Þ. We show that this is not the case, and construct such a set. We prove that this is combinatorially unique. We also complete the spectr...
متن کاملMinimal blocking sets in PG(2, 9)
We classify the minimal blocking sets of size 15 in PG(2, 9). We show that the only examples are the projective triangle and the sporadic example arising from the secants to the unique complete 6-arc in PG(2, 9). This classification was used to solve the open problem of the existence of maximal partial spreads of size 76 in PG(3, 9). No such maximal partial spreads exist [13]. In [14], also the...
متن کاملOn small blocking sets and their linearity
We prove that a small blocking set of PG(2, q) is “very close” to be a linear blocking set over some subfield GF(p) < GF(q). This implies that (i) a similar result holds in PG(n, q) for small blocking sets with respect to k-dimensional subspaces (0 ≤ k ≤ n) and (ii) most of the intervals in the interval-theorems of Szőnyi and Szőnyi-Weiner are empty.
متن کاملCharacterization results on small blocking sets
In [8], De Beule and Storme characterized the smallest blocking sets of the hyperbolic quadrics Q+(2n + 1, 3), n ≥ 4; they proved that these blocking sets are truncated cones over the unique ovoid of Q+(7, 3). We continue this research by classifying all the minimal blocking sets of the hyperbolic quadrics Q+(2n + 1, 3), n ≥ 3, of size at most 3n + 3n−2. This means that the three smallest minim...
متن کاملSmall Blocking Sets in Higher Dimensions
We show that small blocking sets in PG(n, q) with respect to hyperplanes intersect every hyperplane in 1 modulo p points, where q= p. The result is then extended to blocking sets with respect to k-dimensional subspaces and, at least when p>2, to intersections with arbitrary subspaces not just hyperplanes. This can also be used to characterize certain non-degenerate blocking sets in higher dimen...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2002
ISSN: 0195-6698
DOI: 10.1006/eujc.2001.0545