Sharp density bounds on the finite field Kakeya
Boris Bukh, Ting-Wei Chao · arXiv (Cornell University) · 2021
A Kakeya set in $\mathbb{F}_q^n$ is a set containing a line in every direction. We show that every Kakeya set in $\mathbb{F}_q^n$ has density at least $1/2^{n-1}$, matching the construction by Dvir, Kopparty, Saraf and Sudan.