Given a set system $$(X, \mathcal {R})$$ such that every pair of sets in $$\mathcal {R}$$ have large symmetric difference, the Shallow Packing Lemma gives an upper bound on $$|\mathcal {R}|$$ as a function of the shallow-cell complexity of $$\mathcal {R}$$ . In this paper, we first present a matching lower bound. Then we give our main theorem, an application of the Shallow Packing Lemma: given a semialgebraic set system $$(X, \mathcal {R})$$ with shallow-cell complexity $$\varphi (\cdot , \cdot )$$ and a parameter $$\epsilon > 0$$ , there exists a collection, called an $$\epsilon $$ -Mnet, consisting of $$O\bigl ( \frac{1}{\epsilon } \,\varphi \bigl ( O\bigl (\frac{1}{\epsilon } \bigr ), O(1)\bigr ) \bigr )$$ subsets of X, each of size $$\Omega ( \epsilon |X| )$$ , such that any $$R \in \mathcal {R}$$ with $$|R| \ge \epsilon |X|$$ contains at least one set in this collection. We observe that as an immediate corollary an alternate proof of the optimal $$\epsilon $$ -net bound follows.