Density of an integral lattice (reviewed)

The density of an $n\times n$ integral lattice is the density of the lattice-centered sphere packing in $\mathbb R^n$.

The lattice packing problem of dimension $n$ is to find the lattices which maximize the density. In general, these may not be solutions of the sphere packing problem, which asks for the maximum density of a sphere packing in which the centers of the spheres need not form an integral lattice.