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 multiple blocking sets in Galois planes
This article continues the study of multiple blocking sets in PG(2, q). In [3], using lacunary polynomials, it was proven that t-fold blocking sets of PG(2, q), q square, t < q1/4/2, of size smaller than t(q + 1) + cqq 2/3, with cq = 2 −1/3 when q is a power of 2 or 3 and cq = 1 otherwise, contain the union of t pairwise disjoint Baer subplanes when t ≥ 2, or a line or a Baer subplane when t = ...
متن کاملGroups With Maximal Irredundant Covers And Minimal Blocking Sets
Let n be a positive integer. Denote by PG(n, q) the n-dimensional projective space over the finite field Fq of order q. A blocking set in PG(n, q) is a set of points that has non-empty intersection with every hyperplane of PG(n, q). A blocking set is called minimal if none of its proper subsets are blocking sets. In this note we prove that if PG(ni, q) contains a minimal blocking set of size ki...
متن کاملThe size of minimal blocking sets of Q(4, q)
Let Q(2n+2, q) denote the non-singular parabolic quadric in the projective geometry PG(2n+2, q). We describe the implementation in GAP of an algorithm to determine the minimal number of points of a minimal blocking set of Q(4, q), for q = 5, 7
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2018
ISSN: 1077-8926
DOI: 10.37236/7810