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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
##### Keywords:
Kakeya set; finite vector space; finite fields; value set
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