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On the construction of dense lattices with a given automorphisms group

Philippe Gaborit, Gilles Zémor (2007)

Annales de l’institut Fourier

We consider the problem of constructing dense lattices in n with a given non trivial automorphisms group. We exhibit a family of such lattices of density at least c n 2 - n , which matches, up to a multiplicative constant, the best known density of a lattice packing. For an infinite sequence of dimensions n , we exhibit a finite set of lattices that come with an automorphisms group of size n , and a constant proportion of which achieves the aforementioned lower bound on the largest packing density. The algorithmic...

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