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A Note on Optimal Unimodular Lattices

J. H. Conway·N. J. A. Sloane
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Abstract

The highest possible minimal norm of a unimodular lattice is determined in dimensions n <= 33. There are precisely five odd 32-dimensional lattices with the highest possible minimal norm (compared with more than 8*10^20 in dimension 33). Unimodular lattices with no roots exist if and only if n >= 23, n not = 25.

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J. H. Conway, N. J. A. Sloane. 2002-07-31. A Note on Optimal Unimodular Lattices. https://arxiv.org/abs/math/0207292

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