Unit Sphere Packings and Coverings of the Hamming Space

A new method of construction of sphere packings and coverings is used to prove that the density of the best unit sphere coverings and packings of the $n$-dimensional Hamming space goes to 1 as $n\to\infty$. The proposition proved about packings is equivalent to asymptotic exactness of the Hamming bound on the cardinality of single-error-correcting codes.