Kakeya-type sets in finite vector spaces

Details Kakeya-type sets in finite vector spaces Kakeya-type sets in finite vector spaces

2010-03-19

arxiv.org/abs/1003.3736v1

Mathematics

Number Theory

Scientific paper

For a finite vector space $V$ and a non-negative integer $r\le\dim V$ we estimate the smallest possible size of a subset of $V$, containing a translate of every $r$-dimensional subspace. In particular, we show that if $K\subset V$ is the smallest subset with this property, $n$ denotes the dimension of $V$, and $q$ is the size of the underlying field, then for $r$ bounded and $r

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