Abstract
A lattice is a finitely generated discrete subgroup of Euclidean space. Lattices are an important algorithmic tool in number theory, integral representation theory, geometry, information theory, cryptography, crystallography and have various other applications within mathematics and beyond. Any lattice has only finitely many vectors of a given length, they form the layers of the lattice, which are finite subsets of spheres in the underlying Euclidean space.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Nebe, G. (2010). Lattices and Spherical Designs. In: Hanrot, G., Morain, F., Thomé, E. (eds) Algorithmic Number Theory. ANTS 2010. Lecture Notes in Computer Science, vol 6197. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14518-6_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-14518-6_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14517-9
Online ISBN: 978-3-642-14518-6
eBook Packages: Computer ScienceComputer Science (R0)