Improved lower bound on the size of Kakeya sets over finite fields

2008/08/18 by Saraf, Shubhangi, Sudan, Madhu · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.0808.2499

Abstract

In a recent breakthrough, Dvir showed that every Kakeya set in \Fⁿ must be of cardinality at least c_n |\F|ⁿ where c_n ≈ 1/n!. We improve this lower bound to βⁿ |\F|ⁿ for a constant β> 0. This pins down the growth of the leading constant to the right form as a function of n.

Cited by

• On an analogue of BRK-type sets in finite fields

Related

• On the size of Kakeya sets in finite vector spaces
• Size of local finite field Kakeya sets
• Maximal and (m,ε)-Kakeya bounds over ℤ/Nℤ for general N
• A lower bound for the size of Kakeya sets with respect to hyperplanes in \mathbbF_qⁿ
• Conical Kakeya and Nikodym Sets in Finite Fields