  In this paper I will approach the computation of the maximum density of
regular lattices in large dimensions using a statistical mechanics approach.
The starting point will be some theorems of Roger, which are virtually unknown
in the community of physicists. Using his approach one can see that there are
many similarities (and differences) with the problem of computing the entropy
of a liquid of perfect spheres. The relation between the two problems is
investigated in details. Some conjectures are presented, that need further
investigation in order to check their consistency.
