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

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

2008-08-18

arxiv.org/abs/0808.2499v2

Mathematics

Combinatorics

4 pages, Appendix with upper bound added

Scientific paper

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

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