A note on strong blocking sets and higgledy-piggledy sets of lines
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917587172982784 |
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| author | Lia, Stefano Van de Voorde, Geertrui |
| author_facet | Lia, Stefano Van de Voorde, Geertrui |
| contents | This paper studies {\em 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 {\em higgledy-piggledy arrangement}; thus giving rise to a strong blocking set of size $(2N-2)(q+1)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_06939 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on strong blocking sets and higgledy-piggledy sets of lines Lia, Stefano Van de Voorde, Geertrui Combinatorics This paper studies {\em 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 {\em higgledy-piggledy arrangement}; thus giving rise to a strong blocking set of size $(2N-2)(q+1)$. |
| title | A note on strong blocking sets and higgledy-piggledy sets of lines |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2402.06939 |