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