Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
MathSciNet review: 1466959
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 52C17, 11H31, 94B15

Retrieve articles in all journals with MSC (1991): 52C17, 11H31, 94B15


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: http://dx.doi.org/10.1090/S0002-9947-99-02169-8
PII: S 0002-9947(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