We prove detailed asymptotics for the number of spanning trees, called
complexity, for a general class of discrete tori as the parameters tend to
infinity. The proof uses in particular certain ideas and techniques from an
earlier paper. Our asymptotic formula provides a link between the complexity of
these graphs and the height of associated real tori, and allows us to deduce
some corollaries on the complexity thanks to certain results from analytic
number theory. In this way we obtain a conjectural relationship between
complexity and regular sphere packings.Comment: 14 page
