A Note on Optimal Unimodular Lattices
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*1020 in dimension 33). Unimodular lattices with no roots exist if and only if n >= 23, n not = 25.
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