$. As described in Lemma \[ballcover\], $\bar{S}$ can be covered by $0^d$ hypercubes of side length $0 r_0$, the union of which we shall refer to as $H$. Set $L = (\mu+0)\sqrt{d}$. Imagine a partition of $H$ into a grid, where each cell is of side-length $\frac{r_0}{L}$