English

The maximum and the minimum size of complete (n,3)-arcs in PG(2,16)

Combinatorics 2012-01-12 v1
Authors: Daniele Bartoli , Stefano Marcugini , Fernanda Pambianco
View on arXiv ↗ PDF ↗

Abstract

In this work we solve the packing problem for complete (n,3)-arcs in PG(2,16), determining that the maximum size is 28 and the minimum size is 15. We also performed a partial classification of the extremal size of complete (n,3)-arcs in PG(2,16).

Keywords

complete (n,3)-arcs PG(2,16) packing problem finite projective plane extremal size

Cite

@article{arxiv.1201.2260,
  title  = {The maximum and the minimum size of complete (n,3)-arcs in PG(2,16)},
  author = {Daniele Bartoli and Stefano Marcugini and Fernanda Pambianco},
  journal= {arXiv preprint arXiv:1201.2260},
  year   = {2012}
}

Comments

3 pages

Related papers

View all related →
Combinatorics · Mathematics
Minimal complete arcs in PG(2,q), q<= 32
Stefano Marcugini, Alfredo Milani, Fernanda Pambianco
2010-05-20
Combinatorics · Mathematics
New sizes of complete arcs in PG(2,q)
Alexander A. Davydov, Giorgio Faina, Stefano Marcugini, Fernanda Pambianco
2010-08-31
Combinatorics · Mathematics
Update: Some new results on lower bounds on $(n,r)$-arcs in $PG(2,q)$ for $q\le 31$
Michael Braun
2021-06-11
Combinatorics · Mathematics
Maximal (120,8)-arcs in projective planes of order 16 and related designs
Vladimir D. Tonchev, Tim Wagner
2019-01-29
Combinatorics · Mathematics
New lower bounds on the size of (n,r)-arcs in PG(2,q)
Michael Braun
2019-07-19
Combinatorics · Mathematics
On sizes of complete arcs in PG(2,q)
Daniele Bartoli, Alexander A. Davydov, Giorgio Faina, Stefano Marcugini +1
2011-05-24
Combinatorics · Mathematics
Partitions of AG(4,3) into Maximal Caps
Michael Follett, Kyle Kalail, Elizabeth McMahon, Catherine Pelland +1
2018-08-28
Combinatorics · Mathematics
Hyperfocused arcs in PG(2,32)
Giorgio Faina, Cristiano Parrettini, Fabio Pasticci
2011-02-22
Combinatorics · Mathematics
Completeness of cubic curves in PG(2, q), q <= 81
Daniele Bartoli, Stefano Marcugini, Fernanda Pambianco
2015-10-29
Combinatorics · Mathematics
On the Maximum Number of Edges in a Hypergraph with Given Matching Number
Peter Frankl
2012-06-01
Combinatorics · Mathematics
Algebraic constructions of complete $m$-arcs
Daniele Bartoli, Giacomo Micheli
2020-07-03
Metric Geometry · Mathematics
Dense Packings of Congruent Circles in Rectangles with a Variable Aspect Ratio
Boris D. Lubachevsky, Ronald Graham
2007-05-23
Combinatorics · Mathematics
A computer search of maximal partial spreads in PG(3,q)
Maurizio Iurlo, Sandro Rajola
2011-11-15
Combinatorics · Mathematics
Tables of sizes of random complete arcs in the plane $PG(2,q)$
Daniele Bartoli, Alexander A. Davydov, Giorgio Faina, Stefano Marcugini +1
2014-05-23
Combinatorics · Mathematics
Tables, bounds and graphics of the smallest known sizes of complete arcs in the plane $\mathrm{PG}(2,q)$ for all $q\le160001$ and sporadic $q$ in the interval $[160801\ldots 430007]$
Daniele Bartoli, Alexander A. Davydov, Giorgio Faina, Alexey A. Kreshchuk +2
2015-06-30
Combinatorics · Mathematics
Semiovals in PG(2,8) and PG(2,9)
Daniele Bartoli, Stefano Marcugini, Fernanda Pambianco
2013-12-10
Combinatorics · Mathematics
Upper bounds on the smallest size of a complete arc in the plane PG(2,q)
Daniele Bartoli, Alexander A. Davydov, Giorgio Faina, Stefano Marcugini +1
2011-11-16
Combinatorics · Mathematics
Classification of large partial plane spreads in $PG(6,2)$ and related combinatorial objects
Thomas Honold, Michael Kiermaier, Sascha Kurz
2018-12-17
Combinatorics · Mathematics
Tables, bounds and graphics of the smallest known sizes of complete caps in the spaces $\mathrm{PG}(3,q)$ and $\mathrm{PG}(4,q)$
Daniele Bartoli, Alexander A. Davydov, Alexey A. Kreshchuk, Stefano Marcugini +1
2016-11-01
Combinatorics · Mathematics
Optimal Packings of 22 and 33 Unit Squares in a Square
Wolfram Bentz
2016-06-14
Metric Geometry · Mathematics
Minimum Perimeter Rectangles That Enclose Congruent Non-Overlapping Circles
Boris D. Lubachevsky, Ronald L. Graham
2009-04-03
Combinatorics · Mathematics
Augmenting Geometric Graphs with Matchings
Alexander Pilz, Jonathan Rollin, Lena Schlipf, André Schulz
2020-08-20
Combinatorics · Mathematics
$2$-arcs of maximal size in the affine and the projective Hjelmslev plane over $\mathbb{Z}_{25}$
Michael Kiermaier, Matthias Koch, Sascha Kurz
2014-01-21
Metric Geometry · Mathematics
Packing-constrained point coverings
Veit Elser
2011-01-19
Combinatorics · Mathematics
On the packing for triples
Ramin Javadi, Ehsan Poorhadi, Farshad Fallah
2019-05-28