  Motivated by long-standing conjectures on the discretization of classical
inequalities in the Geometry of Numbers, we investigate a new set of
parameters, which we call \emph{packing minima}, associated to a convex body
$K$ and a lattice $\Lambda$. These numbers interpolate between the successive
minima of $K$ and the inverse of the successive minima of the polar body of
$K$, and can be understood as packing counterparts to the covering minima of
Kannan & Lov\'{a}sz (1988). As our main results, we prove sharp inequalities
that relate the volume and the number of lattice points in $K$ to the sequence
of packing minima. Moreover, we extend classical transference bounds and
discuss a natural class of examples in detail.

Metric Geometry;Combinatorics