Dense sphere-packings (Q2918933)
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scientific article; zbMATH DE number 6089141
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Dense sphere-packings |
scientific article; zbMATH DE number 6089141 |
Statements
1 October 2012
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sphere packing
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density
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Kepler conjecture
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kissing number
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lattice
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signal transmission
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error correction
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Leech packing
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Dense sphere-packings (English)
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The author introduces some problems of sphere packing to non-mathematicians. After motivating the subject by describing Kepler packings in \(\mathbb R^3\), she gives definitions of metrics, Euclidean and Hamming spaces, balls, ball packings (or sphere packings) and their densities. The use of dense sphere packings for error correction in signal transmission is pointed out. A particular emphasis is on Euclidean sphere packings that are arranged along lattices. Optimal densities of such packings are stated for dimensions \(n \leq 8\) and \(n=24\) and are compared with the case that the underlying lattice is \(\mathbb Z^n\). Finally, symmetries of lattice packings serve as a link to group theory.NEWLINENEWLINEFor the entire collection see [Zbl 1222.00035].
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