New Packings on a Finite-Dimensional Euclidean Sphere

A spherical code is a finite set of points in a sphere of radius 1 in the $n$-dimensional Euclidean space with a given minimum distance $\rho$. The cardinality of the best spherical code with distance $\rho=1$ is called the contact number $\tau_n$. Leech and Sloane (1971) demonstrated how to construct spherical codes using binary block cods (both constant-weight and ordinary). Here we propose new constructions that improve the lower bounds on the cardinality of spherical codes with $\rho\leq 1$ for $n\leq 64$.