Vol. 8, No. 2, 2019

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Lattices with exponentially large kissing numbers

Serge Vlăduţ

Vol. 8 (2019), No. 2, 163–177
Abstract

We construct a sequence of lattices {Lni ni} for ni with exponentially large kissing numbers, namely, log2τ(Lni) > 0.0338 ni o(ni). We also show that the maximum lattice kissing number τnl in n dimensions satisfies log2τnl > 0.0219 n o(n) for any n.

Keywords
lattices, algebraic geometry codes, kissing numbers, Drinfeld modular curves
Mathematical Subject Classification 2010
Primary: 11H31, 11H71, 14G15, 52C17
Milestones
Received: 22 August 2018
Revised: 3 October 2018
Accepted: 18 October 2018
Published: 20 May 2019
Authors
Serge Vlăduţ
Aix Marseille Université, CNRS
Centrale Marseille
I2M UMR 7373
Marseille
France
IITP RAS
Moscow
Russia