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

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