This paper studies strong blocking sets in the $N$-dimensional finite projective space $\mathrm{PG}(N,q)$. We first show that certain unions of blocking sets cannot form strong blocking sets, which leads to a new lower bound on the size of a strong blocking set in $\mathrm{PG}(N,q)$. Our second main result shows that, for $q>\frac{2}{\ln(2)}(N+1)$, there exists a subset of $2N-2$ lines of a Desarguesian line spread in $\mathrm{PG}(N,q)$, $N$ odd, in higgledy-piggledy arrangement; thus giving rise to a strong blocking set of size $(2N-2)(q+1)$.
@article{10_37236_12790,
author = {Stefano Lia and Geertrui Van de Voorde},
title = {A note on strong blocking sets and higgledy-piggledy sets of lines},
journal = {The electronic journal of combinatorics},
year = {2025},
volume = {32},
number = {3},
doi = {10.37236/12790},
zbl = {8097655},
url = {http://geodesic.mathdoc.fr/articles/10.37236/12790/}
}
TY - JOUR
AU - Stefano Lia
AU - Geertrui Van de Voorde
TI - A note on strong blocking sets and higgledy-piggledy sets of lines
JO - The electronic journal of combinatorics
PY - 2025
VL - 32
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/12790/
DO - 10.37236/12790
ID - 10_37236_12790
ER -
%0 Journal Article
%A Stefano Lia
%A Geertrui Van de Voorde
%T A note on strong blocking sets and higgledy-piggledy sets of lines
%J The electronic journal of combinatorics
%D 2025
%V 32
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/12790/
%R 10.37236/12790
%F 10_37236_12790
Stefano Lia; Geertrui Van de Voorde. A note on strong blocking sets and higgledy-piggledy sets of lines. The electronic journal of combinatorics, Tome 32 (2025) no. 3. doi: 10.37236/12790
