#### Vol. 1, No. 3, 2008

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An improved lower bound on the size of Kakeya sets over finite fields

### Shubhangi Saraf and Madhu Sudan

Vol. 1 (2008), No. 3, 375–379
##### Abstract

In a recent breakthrough, Dvir showed that every Kakeya set in ${\mathbb{F}}^{n}$ must have cardinality at least ${c}_{n}|\mathbb{F}{|}^{n}$, where ${c}_{n}\approx 1∕n!$. We improve this lower bound to ${\beta }^{n}|\mathbb{F}{|}^{n}$ for a constant $\beta >0$. This pins down the correct growth of the constant ${c}_{n}$ as a function of $n$ (up to the determination of $\beta$).

##### Keywords
Kakeya set, finite fields, polynomial method
Primary: 52C17
Secondary: 05B25