Biangular lines revisited

Abstract

Line systems passing through the origin of the $d$ dimensional Euclidean space admitting exactly two distinct angles are called biangular. It is shown that the maximum cardinality of biangular lines is at least $2(d-1)(d-2)$, and this result is sharp for $d\in\{4,5,6\}$. Connections to binary codes, few-distance sets, and association schemes are explored, along with their multiangular generalization.