In this article, we examine sets of lines in $\mathsf{PG}(d,\mathbb{F})$ meeting each hyperplane in a generator set of points. We prove that such a set has to contain at least $\lfloor1.5d\rfloor$ lines if the field $\mathbb{F}$ has at least $\lfloor1.5d\rfloor$ elements, and at least $2d-1$ lines if the field $\mathbb{F}$ is algebraically closed. We show that suitable $2d-1$ lines constitute such a set (if $|\mathbb{F}|\ge2d-1$), proving that the lower bound is tight over algebraically closed fields. At last, we will see that the strong $(s,A)$ subspace designs constructed by Guruswami and Kopparty have better (smaller) parameter $A$ than one would think at first sight.
@article{10_37236_4149,
author = {Szabolcs L. Fancsali and P\'eter Sziklai},
title = {Lines in higgledy-piggledy arrangement},
journal = {The electronic journal of combinatorics},
year = {2014},
volume = {21},
number = {2},
doi = {10.37236/4149},
zbl = {1300.05049},
url = {http://geodesic.mathdoc.fr/articles/10.37236/4149/}
}
TY - JOUR
AU - Szabolcs L. Fancsali
AU - Péter Sziklai
TI - Lines in higgledy-piggledy arrangement
JO - The electronic journal of combinatorics
PY - 2014
VL - 21
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/4149/
DO - 10.37236/4149
ID - 10_37236_4149
ER -
%0 Journal Article
%A Szabolcs L. Fancsali
%A Péter Sziklai
%T Lines in higgledy-piggledy arrangement
%J The electronic journal of combinatorics
%D 2014
%V 21
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/4149/
%R 10.37236/4149
%F 10_37236_4149
Szabolcs L. Fancsali; Péter Sziklai. Lines in higgledy-piggledy arrangement. The electronic journal of combinatorics, Tome 21 (2014) no. 2. doi: 10.37236/4149
