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.


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