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arXiv · 2206.11189

An algorithm to count the number of caps in $\mathbb{P}^3(\mathbb{F}_q)$

Kelly Isham
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Abstract

An $n$-cap in $k$-dimensional projective space is a set of $n$ points so that no three lie on a line. In this note, we provide an algorithm to count the number of $n$-caps in $\mathbb{P}^3(\mathbb{F}_q)$, which follows from our recent paper [9]. We then give exact formulas for the number of $n$-caps when $n \le 7$. The formulas are polynomial in $q$ when $n \le 6$ and quasipolynomial in $q$ when $n = 7$.

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Kelly Isham. 2022-06-22. An algorithm to count the number of caps in $\mathbb{P}^3(\mathbb{F}_q)$. https://arxiv.org/abs/2206.11189

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