Multiple blocking sets in PG ( 2 , 23 ) 1 Rumen
نویسنده
چکیده
An (n, r)-arc is a set of n points of a projective plane such that some r, but no r + 1 of them, are collinear. The maximum size of an (n, r)-arc in PG(2, q) is denoted by mr(2, q). Using some good blocking sets in PG(2, 23) we establish that m22(2, 23) ≥ 484, m21(2, 23) ≥ 461, m20(2, 23) ≥ 437, m19(2, 23) ≥ 411, m18(2, 23) ≥ 385 and m17(2, 23) ≥ 360.
منابع مشابه
On 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 کاملThe use of blocking sets in Galois geometries and in related research areas
Blocking sets play a central role in Galois geometries. Besides their intrinsic geometrical importance, the importance of blocking sets also arises from the use of blocking sets for the solution of many other geometrical problems, and problems in related research areas. This article focusses on these applications to motivate researchers to investigate blocking sets, and to motivate researchers ...
متن کاملBlocking sets in PG ( 2 , q n ) from cones of PG ( 2 n , q )
Let and B̄ be a subset of = PG(2n − 1, q) and a subset of PG(2n, q) respectively, with ⊂ PG(2n, q) and B̄ ⊂ . Denote by K the cone of vertex and base B̄ and consider the point set B defined by B = (K\ ) ∪ {X ∈ S : X ∩ K = ∅}, in the André, Bruck-Bose representation of PG(2, qn) in PG(2n, q) associated to a regular spread S of PG(2n − 1, q). We are interested in finding conditions on B̄ and in order...
متن کاملBlocking Sets and Derivable Partial Spreads
We prove that a GF(q)-linear Rédei blocking set of size qt + qt−1 + · · · + q + 1 of PG(2, qt ) defines a derivable partial spread of PG(2t − 1, q). Using such a relationship, we are able to prove that there are at least two inequivalent Rédei minimal blocking sets of size qt + qt−1 + · · · + q + 1 in PG(2, qt ), if t ≥ 4.
متن کاملMultiple blocking sets and arcs in finite planes
This paper contains two main results relating to the size of a multiple blocking set in PG(2, q). The first gives a very general lower bound, the second a much better lower bound for prime planes. The latter is used to consider maximum sizes of (k, n)-arcs in PG(2, 11) and PG(2, 13), some of which are determined. In addition, a summary is given of the value of mn(2, q) for q ≤ 13.
متن کامل