  A discrete frame for $L^2({\mathbb R}^d)$ is a countable sequence
$\{e_j\}_{j\in J}$ in $L^2({\mathbb R}^d)$ together with real constants
$0<A\leq B< \infty$ such that $$ A\|f\|_2^2 \leq \sum_{j\in J}|\langle f,e_j
\rangle |^2 \leq B\|f\|_2^2,$$ for all $f\in L^2(\mathbb{R}^d)$. We present a
method of sampling continuous frames, which arise from square-integrable
representations of affine-type groups, to create discrete frames for
high-dimensional signals. Our method relies on partitioning the ambient space
by using a suitable "tiling system". We provide all relevant details for
constructions in the case of ${\rm M}_n({\mathbb R})\rtimes {\rm GL}_n({\mathbb
R})$, although the methods discussed here are general and could be adapted to
many other settings. Finally, we prove significantly improved frame bounds over
the previously known construction for the case of $n=2$.
