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How to find the size of an ϵ-net of a vector space?

Note that $\mathcal{W}_{\epsilon}$ is an epsilon-net in the parametrization space, which is just $p$-dimensional Euclidean space. (So there is no need to think about covering numbers in e.g. spaces of ...
The answer depends on whether you want a bound for a single, fixed $Q\subseteq M$ or uniformly over all such $Q$. For a single, fixed $Q$, the Chernoff-Hoeffding bound is essentially the best you can ...