  An $r$-identifying code on a graph $G$ is a set $C\subset V(G)$ such that for
every vertex in $V(G)$, the intersection of the radius-$r$ closed neighborhood
with $C$ is nonempty and different. Here, we provide an overview on codes for
the $n$-dimensional lattice, discussing the case of 1-identifying codes,
constructing a sparse code for the 4-dimensional lattice as well as showing
that for fixed $n$, the minimum density of an $r$-identifying code is
$\Theta(1/r^{n-1})$.
