Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dense generic well-rounded lattices   It is well-known that the densest lattice sphere packings also typically have
the largest kissing numbers. The sphere packing density maximization problem is
known to have a solution among well-rounded lattices, of which the integer
lattice $\mathbb{Z}^n$ is the simplest example. The integer lattice is also an
example of a generic well-rounded lattice, i.e., a well-rounded lattice with a
minimal kissing number. However, the integer lattice has the worst density
among well-rounded lattices. In this paper, the problem of constructing
explicit generic well-rounded lattices with dense sphere packings is
considered. To this end, so-called tame lattices recently introduced by Damir
et al. are utilized. Tame lattices came to be as a generalization of the ring
of integers of certain abelian number fields. The sublattices of tame lattices
constructed in this paper are shown to always result in either a generic
well-rounded lattice or the lattice $A_n$, with density ranging between that of
$\mathbb{Z}^n$ and $A_n$. Further, explicit deformations of some known densest
lattice packings are constructed, yielding a family of generic well-rounded
lattices with densities arbitrarily close to the optimum. In addition to being
an interesting mathematical problem on its own, the constructions are also
motivated from a more practical point of view. Namely, the constructed lattices
provide good candidates for lattice codes used in secure wireless
communications.

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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: cs
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: supr-con