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

Abstract

In a recent breakthrough, Dvir showed that every Kakeya set in [math] must have cardinality at least [math] , where [math] . We improve this lower bound to [math] for a constant [math] . This pins down the correct growth of the constant [math] as a function of [math] (up to the determination of [math] ).