New bounds for multiple packings of Euclidean sphere

Using lower bounds on distance spectrum components of a code on the Euclidean sphere, we improve the known asymptotical upper bounds on the cardinality of multiple packings of the sphere by balls of smaller radii. Let Rn be the n-dimensional Euclidean space, and Sn−1(r) ⊂ Rn be the (closed) Euclidean sphere of radius r with the center in the origin. Let further S̃n−1(r, ā) be the open ball of radius r centered in ā ∈ Rn. Multiple L-packing K(L, t) by balls of radius t is a finite set (≡code) K ⊂ Sn−1(1), such that for any subset {x̄1, . . . , x̄L+1} ⊂ K of L + 1 points (≡codewords) we have