  We introduce an order on the set of non-divisorial ideals of a numerical
semigroup $S$, and link antichains of this order with the star operations on
$S$; subsequently, we use this order to find estimates on the number of star
operations on $S$. We then use them to find an asymptotic estimate on the
number of nonsymmetric numerical semigroups with $n$ or less star operations,
and to determine these semigroups explicitly when $n=10$.
