Moscow Journal of Combinatorics and Number Theory

Lattices with exponentially large kissing numbers

Serge Vlăduţ

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Abstract

We construct a sequence of lattices {Lnini} for ni with exponentially large kissing numbers, namely, log2τ(Lni)>0.0338nio(ni). We also show that the maximum lattice kissing number τnl in n dimensions satisfies log2τnl>0.0219no(n) for any n.

Article information

Source
Mosc. J. Comb. Number Theory, Volume 8, Number 2 (2019), 163-177.

Dates
Received: 22 August 2018
Revised: 3 October 2018
Accepted: 18 October 2018
First available in Project Euclid: 29 May 2019

Permanent link to this document
https://projecteuclid.org/euclid.moscow/1559095391

Digital Object Identifier
doi:10.2140/moscow.2019.8.163

Mathematical Reviews number (MathSciNet)
MR3959884

Zentralblatt MATH identifier
07063273

Subjects
Primary: 11H31: Lattice packing and covering [See also 05B40, 52C15, 52C17] 11H71: Relations with coding theory 14G15: Finite ground fields 52C17: Packing and covering in $n$ dimensions [See also 05B40, 11H31]

Keywords
lattices algebraic geometry codes kissing numbers Drinfeld modular curves

Citation

Vlăduţ, Serge. Lattices with exponentially large kissing numbers. Mosc. J. Comb. Number Theory 8 (2019), no. 2, 163--177. doi:10.2140/moscow.2019.8.163. https://projecteuclid.org/euclid.moscow/1559095391


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