Moscow Journal of Combinatorics and Number Theory
Mosc. J. Comb. Number Theory
Volume 8, Number 2 (2019), 163-177.
Lattices with exponentially large kissing numbers
Serge Vlăduţ
More by Serge Vlăduţ
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We construct a sequence of lattices {Lni⊂ℝni} 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.
Mosc. J. Comb. Number Theory, Volume 8, Number 2 (2019), 163-177.
Revised: 3 October 2018
First available in Project Euclid: 29 May 2019
https://projecteuclid.org/euclid.moscow/1559095391
doi:10.2140/moscow.2019.8.163
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]
lattices algebraic geometry codes kissing numbers Drinfeld modular curves
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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