On the size of Kakeya sets in finite fields
classification
🧮 math.CO
math.CAmath.NT
keywords
kakeyaeveryfinitesizebestboundcontainsdepends
read the original abstract
A Kakeya set is a subset of F^n, where F is a finite field of q elements, that contains a line in every direction. In this paper we show that the size of every Kakeya set is at least C_n * q^n, where C_n depends only on n. This improves the previously best lower bound for general n of ~q^{4n/7}.
This paper has not been read by Pith yet.
Forward citations
Cited by 1 Pith paper
-
Transversal Difference Numbers in Finite Abelian Quotients
Introduces δ(G,H) for finite abelian quotients, proves δ(G,H) ≥ 2|G/H| - m(G,H) sharp for cyclic cases, and conjectures δ=(2p-1)² for the (Z/p²Z)² case with lower bound 3p²-p-1.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.