During my internship at the Mayo Clinic in 2007, I did some work to
make generating lattices for sphere packing easier. I have revisited
the problem often.
Here are my two short articles on the topic:
Sphere Packing Lattice Generation, August 16, 2007 orginally found at http://porlamadrugada.googlepages.com/AlecJacobsonSpherePacking.pdf.
More on Sphere Packing, January 24, 2008
I have also incorporated this work into a ray-tracing java applet.
Maximal Sphere Packing, August 8, 2010, This is a work in progress, forming around the problem of finding the maximal choices of radii and number of spheres to pack a given volume (using a lattice).
The Close packing of spheres article on wikipedia reflects my and others' participation in the online collaborative efforts to clarify this topic.