Equiangular lines in Euclidean spaces: dimensions 17 and 18

Abstract

We show that the maximum cardinality of an equiangular line system in 17 dimensions is 48, thereby solving a longstanding open problem. Furthermore, by giving an explicit construction, we improve the lower bound on the maximum cardinality of an equiangular line system in 18 dimensions to 57.

Keywords

• Equiangular lines
• dimensions 17 and 18
• compatible polynomials
• eigenspace angles
• polynomial interlacing