Empilements de sphères. (Sphere packings). (French) Zbl 0731.52005

Oesterlé, Joseph

Sémin. Bourbaki, Vol. 1989/90, 42ème année, Astérisque 189-190, Exp. No. 727, 375-397 (1990).

[For the entire collection see Zbl 0722.00001.]
The author investigates a method by Elkies and Shioda based on the arithmetic of elliptic curves to find densest lattice packings of spheres in euclidean d-space. The method is powerful enough to improve the best known densities for the following dimensions: 54, 64, 80, 104, 128, 256, 508, 512, 520, and 1024.

Reviewer: J.M.Wills (Siegen)

MSC:

52C17	Packing and covering in \(n\) dimensions (aspects of discrete geometry)
14H52	Elliptic curves
11H31	Lattice packing and covering (number-theoretic aspects)
05B40	Combinatorial aspects of packing and covering

Keywords:

densest lattice packings; spheres; euclidean d-space

Citations:

Zbl 0722.00001