  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 $n = 7$.
