An algorithm to count the number of caps inℙ³(𝔽_(q))

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 w...

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Bibliographic Details
Main Author Isham, Kelly
Format Journal Article
LanguageEnglish
Published 22.06.2022
Subjects
Mathematics - Combinatorics
Online AccessGet full text
DOI10.48550/arxiv.2206.11189

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Summary: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$n = 7$ .
DOI:10.48550/arxiv.2206.11189