Réseaux ayant beaucoup de vecteurs minimaux

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Date(s) - 24/05/2018
11 h 00 min - 12 h 00 min

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We construct a sequence of lattices $\{L_{n_i}\subset\mathbb{R}^{n_i}\}$ for $n_i\longrightarrow \infty$, with exponentially large kissing numbers, namely, $\log_2 \tau(L_{n_i})/n_i > 0.0338 – o(1)$. We also show that the maximum lattice kissing number $ \tau^l(n)$ in $n$ dimensions verifies $\lim\inf \log_2\tau^l(n)/n \ge 0.0219$. Before our work the best known bound was quasipolynomial, $\tau^l(n) = \Omega( n^{c\log_2 n})$.

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