On extreme forms in dimension 8

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A theorem of Voronoi asserts that a lattice is extreme if and only if it is perfect and eutactic. Very recently the classification of the perfect forms in dimension 8 has been completed. There are 10916 perfect lattices. Using methods of linear programming, we are able to identify those that are additionally eutactic. In lower dimensions almost all perfect lattices are also eutactic (for example 30 out of the 3$ in dimension 7). This is no longer the case in dimension 8: up to similarity, there are only 2408 extreme 8-dimensional lattices.

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ISO 690RIENER, Cordian, 2006. On extreme forms in dimension 8. In: Journal de théorie des nombres de Bordeaux. 2006, 18(3), pp. 677-682. ISSN 1246-7405. Available under: doi: 10.5802/jtnb.565
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@article{Riener2006extre-17359,
  year={2006},
  doi={10.5802/jtnb.565},
  title={On extreme forms in dimension 8},
  number={3},
  volume={18},
  issn={1246-7405},
  journal={Journal de théorie des nombres de Bordeaux},
  pages={677--682},
  author={Riener, Cordian}
}
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