New packings on a finite-dimensional Euclidean sphere (Q1320665)

A spherical code is a finite set of points on a sphere \(S^{n-1}\) of radius 1 with given minimal distance \(\rho\). The largest possible cardinality of a spherical code with \(\rho=1\) is called the contact number \(\tau_n\): It is the largest number of unit balls that can be packed around and in contact with a central unit ball. Leech and Sloane (1971) have shown how spherical codes can be constructed using binary block codes. Their ideas have been developed further into the authors' concatenation methods using a 3-point inner code (1990). Here the authors progress to a 4-point construction method, and obtain improvements in spherical sphere packings with \(\rho\leq 1\) for several values of \(n\leq 64\).