## The Kakeya problem: a gap in the spectrum and classification of the smallest examples

- Aart Blokhuis, Maarten De Boeck, Francesco Mazzocca, Leo Storme
- Des. Codes Cryptography
- 2014

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@inproceedings{Dvir2008OnTS, title={On the size of Kakeya sets in finite fields}, author={Zeev Dvir}, year={2008} }

- Published 2008
DOI:10.1090/S0894-0347-08-00607-3

Let F denote a finite field of q elements. A Kakeya set (also called a Besicovitch set) in F is a set K ⊂ F such that K contains a line in every direction. More formally, K is a Kakeya set if for every x ∈ F there exists a point y ∈ F such that the line Ly,x ≜ {y + a ⋅ x∣a ∈ F} is contained in K. The motivation for studying Kakeya sets over finite fields is to try to better understand the more complicated questions regarding Kakeya sets in R. A Kakeya set K ⊂ R is a compact set containing a… CONTINUE READING

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