Maximal lattice-point sections of convex polytopes

Determine a section of a convex body, and in particular of a lattice polytope in dimensions three and higher, that contains the maximum possible number of lattice points among all sections.

Background

The paper studies lattice diameter segments as the two-dimensional instance of the problem of finding sections containing as many lattice points as possible. The authors note that algorithmic methods exist for maximizing Euclidean section volume in convex polytopes, whereas the corresponding discrete optimization problem for lattice points is unresolved in general. Their polynomial-time algorithm solves the planar case by reducing it to the computation of a lattice diameter segment, but it does not resolve the higher-dimensional problem.