Finite sphere packings and the methods of Blichfeldt and Rankin (Q1297818)

The author derives an upper bound for the density of finite sphere packing. That way, interesting Blichfeldt-type and Rankin-type theorems with a special parameter are obtained providing good bounds for finite packing. As the author mentions, the purpose of this paper is not to get a best result, but to show that Blichfeldt's and Rankin's methods lead in a simple and natural way to results in terms of parametric density. Examples of Sidelnikov, Kabatjanski and Levenstein are also considered.