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Algebro-geometric and number-theoretic packings of balls in \({\mathbb{R}}^ n\). (English. Russian original) Zbl 0578.10037
Russ. Math. Surv. 40, No. 2, 219-220 (1985); translation from Usp. Mat. Nauk 40, No. 2(242), 185-186 (1985).
Let \(\lambda_ N=-(1/N) \log_ 2 \Delta\) be the exponent of the packing density \(\Delta\) of non-overlapping open balls of the same radii in \({\mathbb{R}}^ N\). The paper states that the packings and lattices can be constructed with exponents of densities \(\lambda_ N\leq 1.31\) and \(\lambda_ N\leq 2.30\), respectively.
Reviewer: T.V.Vepkhvadze

MSC:
11H31 Lattice packing and covering (number-theoretic aspects)
52C17 Packing and covering in \(n\) dimensions (aspects of discrete geometry)
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