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The dual lattice of an extreme six-dimensional lattice

Part of: Geometry of numbers

Published online by Cambridge University Press:  09 April 2009

David Coulson
David Coulson
Affiliation:
Monash University Clayton, Victoria 3168, Australia
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Abstract

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The best lattice quantizers seem to be duals of extreme lattices. The quantizing constant associated with the dual lattice of Barnes's senary form φ6 is found, together with a new type of quantizing technique. The quantizing constant is better than expected in the sense that it is better than D*6 even though D6 provides a denser packing. This is the smallest dimension for which this occurs.

MSC classification

Secondary: 11H06: Lattices and convex bodies 11H55: Quadratic forms (reduction theory, extreme forms, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 50 , Issue 3 , June 1991 , pp. 373 - 383
Copyright
Copyright © Australian Mathematical Society 1991

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