  For a fixed dimension $N$ we compute the generating function of the numbers
$t_N(n)$ (respectively $\bar{t}_N(n)$) of $PGL_{N+1}(k)$-orbits of rational
$n$-sets (respectively rational $n$-multisets) of the projective space
$\mathb{P}^N$ over a finite field $k=\mathbb{F}_q$. For $N=1,2$ these results
provide concrete formulas for $t_N(n)$ and $\bar{t}_N(n)$ as a polynomial in
$q$ with integer coefficients.
