  A numerical set is a co-finite subset of the natural numbers that contains
zero. Its Frobenius number is the largest number in its complement. Each
numerical set has an associated semigroup $A(T)=\{t\mid t+T\subseteq T\}$,
which has the same Frobenius number as $T$. For a fixed Frobenius number $f$
there are $2^{f-1}$ numerical sets. It is known that there is a number $\gamma$
close to $0.484$ such that the ratio of these numerical sets that are mapped to
$N_f=\{0\}\cup(f,\infty)$ is asymptotically $\gamma$. We identify a collection
of families $N(D,f)$ of numerical semigroups such that for a fixed $D$ the
ratio of the $2^{f-1}$ numerical sets that are mapped to $N(D,f)$ converges to
a positive limit as $f$ goes to infinity. We denote the limit as $\gamma_D$,
these constants sum up to $1$ meaning that they asymptotically account for
almost all numerical sets.
