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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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A Gilbert-Varshamov type bound for Euclidean packings
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by Gabriele Nebe and Chaoping Xing PDF
Math. Comp. 77 (2008), 2339-2344 Request permission

Abstract:

This paper develops a method to obtain a Gilbert-Varshamov type bound for dense packings in the Euclidean spaces using suitable lattices. For the Leech lattice the obtained bounds are quite reasonable for large dimensions, better than the Minkowski-Hlawka bound, but not as good as the lower bound given by Keith Ball in 1992.
References
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  • Gabriele Nebe’s homepage, http://www.math.rwth-aachen.de/homes/Gabriele.Nebe/.
  • C. A. Rogers, Packing and covering, Cambridge Tracts in Mathematics and Mathematical Physics, No. 54, Cambridge University Press, New York, 1964. MR 0172183
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Additional Information
  • Gabriele Nebe
  • Affiliation: Lehrstuhl D für Mathematik, RWTH Aachen, Germany
  • MR Author ID: 344248
  • Email: nebe@math.rwth-aachen.de
  • Chaoping Xing
  • Affiliation: Division of Mathematical Science, School of Physical & Mathematical Sciences, Nanyang Technological University, Singapore 637616
  • MR Author ID: 264368
  • Email: xingcp@ntu.edu.sg
  • Received by editor(s): July 3, 2007
  • Received by editor(s) in revised form: October 12, 2007
  • Published electronically: April 28, 2008
  • Additional Notes: The research of the second author was partially supported by the Singapore MoE Tier 1 grant RG60/07 and the National Scientific Research Project 973 of China 2004CB318000
    The second author is the corresponding author
  • © Copyright 2008 American Mathematical Society
  • Journal: Math. Comp. 77 (2008), 2339-2344
  • MSC (2000): Primary 11H31, 52C17, 11H71, 11H06
  • DOI: https://doi.org/10.1090/S0025-5718-08-02113-3
  • MathSciNet review: 2429888