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On the size of Kakeya sets in finite vector spaces. (English) Zbl 1295.11138

Summary: For a finite field \(\mathbb{F}_q\), a Kakeya set \(K\) is a subset of \(\mathbb{F}_q^n\) that contains a line in every direction. This paper derives new upper bounds on the minimum size of Kakeya sets when \(q\) is even.

MSC:

11T30 Structure theory for finite fields and commutative rings (number-theoretic aspects)
11T06 Polynomials over finite fields
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References:

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