Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Perfect, strongly eutactic lattices are periodic extreme   We introduce a parameter space for periodic point sets, given as unions of
$m$ translates of point lattices. 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 periodic sphere packing with
greater density. This applies in particular to the densest known lattice sphere
packings in dimension $d\leq 8$ and $d=24$.

19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
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The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc