AlphaEvolve problems·alphaevolve:1
Kakeya and Nikodym sets in finite fields
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Let $d \\geq 1$, and let $q$ be a prime power. Let $\\mathbb{F}_q$ be a finite field of order $q$. A Kakeya set is a set $K$ that contains a line in every direction, and an Nikodym set $N$ is a set with the property that every point $x$ in $\\mathbb{F}_q^d$ is contained in a line that is contained in $N \\cup \\{x\\}$. Let $C^K(d,q), C^N(d,q)$ denote the least size of a Kakeya or Nikodym set in $\
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