TL;DR
This paper investigates the optimal lattice packings of Minkowski, Davis, and Chebyshev-Cohn balls, showing they are achieved through sublattices of index two of the critical lattices for each ball type.
Contribution
It demonstrates that the best lattice packings for these specific balls are attained via sublattices of index two of their critical lattices, providing new insights into their geometric arrangements.
Findings
Optimal packings are achieved with sublattices of index two.
Critical lattices play a key role in packing efficiency.
Results apply to Minkowski, Davis, and Chebyshev-Cohn balls.
Abstract
In this paper we prove that the optimal lattice packing of the Minkowski, Davis, and Chebyshev-Cohn balls is realized with respect to the sublattices of index two of the critical lattices of corresponding balls
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Taxonomy
TopicsPoint processes and geometric inequalities · Quasicrystal Structures and Properties · Mathematical Dynamics and Fractals