An algorithm to count the number of caps inℙ³(𝔽_(q)) - Isham, Kelly (2022)
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$n = 7$ .