Sphere Packings, Lattices and Groups: 290

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We now apply the algorithm above to find the 121 orbits of norm -2 vectors from the (known) nann 0 vectors, and then apply it again to find the 665 orbits of nann -4 vectors from the vectors of nann 0 and -2. The third edition of this timely, definitive, and popular book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space? The authors also continue to examine related problems such as the kissing number problem, the covering problem, the quantizing problem, and the classification of lattices and quadratic forms. Like the previous edition, the third edition describes the applications of these questions to other areas of mathematics and science such as number theory, coding theory, group theory, analog-to-digital conversion and data compression, n-dimensional crystallography, dual theory and superstring theory in physics. Of special interest to the third edtion is a brief report on some recent developments in the field and an updated and enlarged Supplementary Bibliography with over 800 items.

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Pages: 780, Edition: Third Edition 1999, Hardcover, Springer