Equiangular lines in Euclidean spaces

摘要

We obtain several new results contributing to the theory of real equiangular line systems Among other things, we present a new general lower bound on the maximum number of equiangular lines in d dimensional Euclidean space; we describe the two-graphs on 12 vertices; and we investigate Seidel matrices with exactly three distinct eigenvalues. As a result, we improve on two long-standing upper bounds regarding the maximum number of equiangular lines in dimensions d = 14 and d = 16. Additionally, we prove the nonexistence of certain regular graphs with four eigenvalues, and correct some tables from the literature. (C) 2015 Elsevier Inc. All rights reserved.