A Note on Optimal Unimodular Lattices


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 6= 25.

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@inproceedings{Conway1998ANO, title={A Note on Optimal Unimodular Lattices}, author={John H. Conway}, year={1998} }