Low dimensional strongly perfect lattices . II : Dual strongly perfect lattices of dimension 13 and 15
نویسندگان
چکیده
A lattice is called dual strongly perfect if both, the lattice and its dual, are strongly perfect. We show that there are no dual strongly perfect lattices of dimension 13 and 15.
منابع مشابه
Low dimensional strongly perfect lattices. III: Dual strongly perfect lattices of dimension 14
The extremal 3-modular lattice [±G2(3)]14 with automorphism group C2 × G2(F3) is the unique dual strongly perfect lattice of dimension 14.
متن کاملLow dimensional strongly perfect lattices . I : The 12 - dimensional case
It is shown that the Coxeter-Todd lattice is the unique strongly perfect lattice in dimension 12.
متن کاملBoris Venkov’s Theory of Lattices and Spherical Designs
Boris Venkov passed away on November 10, 2011, just 5 days before his 77th birthday. His death overshadowed the conference “Diophantine methods, lattices, and arithmetic theory of quadratic forms” November 13-18, 2011, at the BIRS in Banff (Canada), where his important contributions to the theory of lattices, modular forms and spherical designs played a central role. This article gives a short ...
متن کاملPerfect, Strongly Eutactic Lattices Are Periodic Extreme
We introduce a parameter space for periodic point sets, given as a union of m translates of a point lattice. In it we investigate the behavior of the sphere packing density function and derive sufficient conditions for local optimality. Using these criteria we prove that perfect, strongly eutactic lattices cannot be locally improved to yield a denser periodic sphere packing. This in particular ...
متن کاملOn extreme forms in dimension 8
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 [5]. 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 ex...
متن کامل