A Gilbert-Varshamov type bound for Euclidean packings |
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| Authors: | Gabriele Nebe Chaoping Xing |
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| Institution: | Lehrstuhl D für Mathematik, RWTH Aachen, Germany ; Division of Mathematical Science, School of Physical & Mathematical Sciences, Nanyang Technological University, Singapore 637616 |
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| 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. |
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