A note on strong blocking sets and higgledy-piggledy sets of lines

2024/02/10 by Stefano Lia, Lia, Stefano, Geertrui Van de Voorde +1
Computer Science · Engineering · #Computational Geometry and Mesh Generation #Advanced Numerical Analysis Techniques #Optimization and Packing Problems

paper · pdf · doi:10.48550/arxiv.2402.06939

Abstract

This paper studies \em strong blocking sets in the N-dimensional finite projective space 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 PG(N,q). Our second main result shows that, for q>(2)/(ln(2))(N+1), there exists a subset of 2N-2 lines of a Desarguesian line spread in PG(N,q), N odd, in \em higgledy-piggledy arrangement; thus giving rise to a strong blocking set of size (2N-2)(q+1).

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