All finite sets are Ramsey in the maximum norm

For two metric spaces $\mathbb X$ and $\mathcal Y$, the chromatic number $\chi(\mathbb X;\mathcal Y)$ of with forbidden Y$ is smallest $k$ such that there a coloring points colors no monochromatic copy Y$. In this paper, we show for each finite space $\mathcal{M}$ contains at least value $\chi\left(\mathbb R^n_\infty; \mathcal M \right)$ grows exponentially $n$. We also provide explicit lower upper bounds some special M$.