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

  title={Improved lower bound on the size of Kakeya sets over finite fields},
  author={Shubhangi Saraf and Madhu Sudan},
In a recent breakthrough, Dvir showed that every Kakeya set in F must be of cardinality at least cn|F| where cn ≈ 1/n!. We improve this lower bound to β|F| for a constant β > 0. This pins down the growth of the leading constant to the right form as a function of n. Let F be a finite field of q elements. Definition 1 (Kakeya Set) A set K ⊆ F is said to be a Kakeya set in F, if for every b ∈ F, there exists a point a ∈ F such that for every t ∈ F, the point a + t · b ∈ K. We show: Theorem 2 There… CONTINUE READING
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