Sphere Packings, Lattices and Groups (Grundlehren Der Mathematischen Wissenschaften, 290)

Rating:
Summary: The book on lattice
Review: This book is devoted to the subject of lattice packings. It is an outstanding book with all pages interesting. It acts as a reference on the subjects of lattices. What you will find:
--Sphere packings, ie the problem of packing spheres in order to maximize density.
--The problem of Kissin numbers: maximize the number of adjacent sphere to a given sphere in a lattice
--Code, design, and Groups
--Error correcting codes
--Leech lattice
--Integral quadratic forms
--Voronoi cell
--many, many other subjects
What you WON'T find in this book:
--The study of Delaunay cells (or holes, L-polytopes) is quite limited
--The study of continuous families of lattice is not done, you won't find the Voronoi memoires here
--There is just one page on computational aspects of lattice

Nevertheless this book is excellent