A new lower bound for the smallest complete (k, n)-arc in $$\mathrm {PG}(2,q)$$ PG ( 2 , q )
نویسندگان
چکیده
منابع مشابه
Upper bounds on the smallest size of a complete arc in the plane PG(2,q)
New upper bounds on the smallest size t2(2, q) of a complete arc in the projective plane PG(2, q) are obtained for q ≤ 9109. From these new bounds it follows that for q ≤ 2621 and q = 2659, 2663, 2683, 2693, 2753, 2801, the relation t2(2, q) < 4.5 √ q holds. Also, for q ≤ 5399 and q = 5413, 5417, 5419, 5441, 5443, 5471, 5483, 5501, 5521, we have t2(2, q) < 4.8 √ q. Finally, for q ≤ 9067 it hold...
متن کاملNew Large (n, r)-arcs in PG(2, q)
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 $m_r(2,q)$. In this paper we present a new $(184,12)$-arc in PG$(2,17),$ a new $(244,14)$-arc and a new $(267,15$)-arc in $PG(2,19).$
متن کاملUpper bounds on the smallest size of a complete cap in $\mathrm{PG}(N, q)$, $N\ge3$, under a certain probabilistic conjecture
In the projective space PG(N, q) over the Galois field of order q, N ≥ 3, an iterative step-by-step construction of complete caps by adding a new point on every step is considered. It is proved that uncovered points are evenly placed on the space. A natural conjecture on an estimate of the number of new covered points on every step is done. For a part of the iterative process, this estimate is ...
متن کاملConjectural upper bounds on the smallest size of a complete cap in PG(N, q), N ≥ 3
In this work we summarize some recent results to be included in a forthcoming paper [2]. In the projective space PG(N, q) over the Galois field of order q, N ≥ 3, an iterative step-by-step construction of complete caps by adding a new point at every step is considered. It is proved that uncovered points are evenly placed in the space. A natural conjecture on an estimate of the number of new cov...
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...
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ژورنال
عنوان ژورنال: Designs, Codes and Cryptography
سال: 2018
ISSN: 0925-1022,1573-7586
DOI: 10.1007/s10623-018-00592-8