The ACO Seminar (2021–2022)

A set K in the n-dimensional vector space $F_q^n$ over finite field $F_q$ is called a Kakeya set if it contains a line in every direction. Dvir proved that the size |K| is at least $c_nq^n$, where $c_n=1/n!$ by using polynomial method. Recently, We improved the bound to $c_n=1/2^{n-1}$, which is the best possible constant.