  Group testing is concerned with identifying $t$ defective items in a set of
$m$ items, where each test reports whether a specific subset of items contains
at least one defective. In non-adaptive group testing, the subsets to be tested
are fixed in advance. By testing multiple items at once, the required number of
tests can be made much smaller than $m$. In fact, for $t \in \mathcal{O}(1)$,
the optimal number of (non-adaptive) tests is known to be $\Theta(\log{m})$.
  In this paper, we consider the problem of non-adaptive group testing in a
geometric setting, where the items are points in $d$-dimensional Euclidean
space and the tests are axis-parallel boxes (hyperrectangles). We present upper
and lower bounds on the required number of tests under this geometric
constraint. In contrast to the general, combinatorial case, the bounds in our
geometric setting are polynomial in $m$. For instance, our results imply that
identifying a defective pair in a set of $m$ points in the plane always
requires $\Omega(m^{3/5})$ tests, and there exist configurations of $m$ points
for which $\mathcal{O}(m^{2/3})$ tests are sufficient, whereas to identify a
single defective point in the plane, $\Theta(m^{1/2})$ tests are always
necessary and sometimes sufficient.
