  We give a new deterministic construction of integer sensing matrices that can
be used for the recovery of integer-valued signals in compressed sensing. This
is a family of $n \times d$ integer matrices, $d \geq n$, with bounded sup-norm
and the property that no $\ell$ column vectors are linearly dependent, $\ell
\leq n$. Further, if $\ell \leq o(\log n)$ then $d/n \to \infty$ as $n \to
\infty$. Our construction comes from particular sets of difference vectors of
point-sets in $\mathbb R^n$ that cannot be covered by few parallel hyperplanes.
We construct examples of such sets on the $0, \pm 1$ grid and use them for the
matrix construction. We also show a connection of our constructions to a simple
version of the Tarski plank problem.

Combinatorics;Numerical Analysis;Metric Geometry;Numerical Analysis