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Transactions of the American Mathematical Society

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Density doubling, double-circulants,
and new sphere packings


Author: Alexander Vardy
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
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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.


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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

DOI: https://doi.org/10.1090/S0002-9947-99-02169-8
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
Article copyright: © Copyright 1999 American Mathematical Society

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