Density doubling, double-circulants, and new sphere packings
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- by Alexander Vardy PDF
- Trans. Amer. Math. Soc. 351 (1999), 271-283 Request permission
Abstract:
New nonlattice sphere packings in dimensions 20, 22, and 44–47 that are denser than the best previously known sphere packings were recently discovered. We extend these results, showing that the density of many sphere packings in dimensions just below a power of 2 can be doubled using orthogonal binary codes. This produces new dense sphere packings in $\mathbb R^n$ for $n = 25,26,\dots ,31$ and $55,56,\dots ,63$. For $n = 27,28,29,30$ the resulting packings are denser than any packing previously known.References
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Additional Information
- Alexander Vardy
- Affiliation: Coordinated Science Laboratory, University of Illinois, Urbana, Illinois 61801
- Address at time of publication: Ecole Supérieure de Science Informatiques, Route des Colles, BP145, 06903 Sophia-Antipolis, France
- MR Author ID: 294226
- ORCID: 0000-0003-3303-9078
- Received by editor(s): January 1, 1997
- Additional Notes: This research was supported by the Packard Foundation Fellowship and by a grant from the National Science Foundation
- © Copyright 1999 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 351 (1999), 271-283
- MSC (1991): Primary 52C17, 11H31, 94B15
- DOI: https://doi.org/10.1090/S0002-9947-99-02169-8
- MathSciNet review: 1466959