P. Lisonek,
New maximal two-distance sets.
Journal of Combinatorial Theory A 77 (1997), 318-338.

A two-distance set in \$E^d\$ is a point set \$X\$ in the \$d\$-dimensional Euclidean space such that the distances between distinct points in \$X\$ assume only two different non-zero values. Based on results from classical distance geometry, we develop an algorithm to classify, for a given \$d\$, all maximal (largest possible) two-distance sets in \$E^d\$. Using this algorithm we have completed the full classification for all \$d\le 7\$, and we have found one set in \$E^8\$ whose maximality follows from Blokhuis' upper bound on sizes of \$s\$-distance sets. While in the dimensions \$d\le 6\$ our classifications confirm the maximality of previously known sets, the results in \$E^7\$ and \$E^8\$ are new. Their counterpart in dimension \$d\ge 10\$ is a set of unit vectors with only two values of inner products in the Lorentz space \$R^{d,1}\$. The maximality of this set again follows from a bound due to Blokhuis.