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Placement of points on a torus and in a plane. (English. Russian original) Zbl 1143.52303

Subbotin, Yu. N. (ed.), Function theory. Transl. from the Russian. Moscow: MAIK Nauka/ Interperiodica. Proc. Steklov Inst. Math. 2005, Suppl. 2, S211-S216 (2005); translation from Tr. Inst. Mat. Mekh. (Ekaterinburg) 11, No. 2, 196-200 (2005).
The author deals with the largest number of points on an \(n\)-dimensional torus with a given minimal pairwise distance. The problem is formulated as the densest packing of congruent balls on the torus. Estimates are given in the first part of the paper. For a special type of lattice spirals in the complex plane the packing radius is determined and the covering radius is estimated.
For the entire collection see [Zbl 1116.42001].

MSC:

52C17 Packing and covering in \(n\) dimensions (aspects of discrete geometry)
68P30 Coding and information theory (compaction, compression, models of communication, encoding schemes, etc.) (aspects in computer science)
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