A blocking set in an affine plane is a set of points $B$ such that every line contains at least one point of $B$. The best known lower bound for blocking sets in arbitrary (non-desarguesian) affine planes was derived in the 1980's by Bruen and Silverman. In this note, we improve on this result by showing that a blocking set of an affine plane of order $q$, $q\geqslant 25$, contains at least $q+\lfloor\sqrt{q}\rfloor+3$ points.
@article{10_37236_7827,
author = {Maarten De Boeck and Geertrui Van de Voorde},
title = {A new lower bound for the size of an affine blocking set},
journal = {The electronic journal of combinatorics},
year = {2018},
volume = {25},
number = {4},
doi = {10.37236/7827},
zbl = {1479.51010},
url = {http://geodesic.mathdoc.fr/articles/10.37236/7827/}
}
TY - JOUR
AU - Maarten De Boeck
AU - Geertrui Van de Voorde
TI - A new lower bound for the size of an affine blocking set
JO - The electronic journal of combinatorics
PY - 2018
VL - 25
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/7827/
DO - 10.37236/7827
ID - 10_37236_7827
ER -
%0 Journal Article
%A Maarten De Boeck
%A Geertrui Van de Voorde
%T A new lower bound for the size of an affine blocking set
%J The electronic journal of combinatorics
%D 2018
%V 25
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/7827/
%R 10.37236/7827
%F 10_37236_7827
Maarten De Boeck; Geertrui Van de Voorde. A new lower bound for the size of an affine blocking set. The electronic journal of combinatorics, Tome 25 (2018) no. 4. doi: 10.37236/7827
