Large Equiangular Sets of Lines in Euclidean Space

Large Equiangular Sets of Lines in Euclidean Space

A construction is given of 29(d + 1) 2 equiangular lines in Euclidean d-space, when d = 3 · 22t−1 − 1 with t any positive integer. This compares with the well known “absolute” upper bound of 12d(d+ 1) lines in any equiangular set; it is the first known constructive lower bound of order d2 . For background and terminology we refer to Seidel [3]. The standard method for obtaining a system of equi...

Equiangular lines in Euclidean spaces

Equiangular Lines and Spherical Codes in Euclidean Space

A family of lines through the origin in Euclidean space is called equiangular if any pair of lines defines the same angle. The problem of estimating the maximum cardinality of such a family in R was extensively studied for the last 70 years. Motivated by a question of Lemmens and Seidel from 1973, in this paper we prove that for every fixed angle θ and sufficiently large n there are at most 2n−...

Equiangular subspaces in Euclidean spaces

A set of lines through the origin is called equiangular if every pair of lines defines the same angle, and the maximum size of an equiangular set of lines in R was studied extensively for the last 70 years. In this paper, we study analogous questions for k-dimensional subspaces. We discuss natural ways of defining the angle between k-dimensional subspaces and correspondingly study the maximum s...

New Bounds for Equiangular Lines and Spherical Two-Distance Sets

The set of points in a metric space is called an s-distance set if pairwise distances between these points admit only s distinct values. Two-distance spherical sets with the set of scalar products {α,−α}, α ∈ [0, 1), are called equiangular. The problem of determining the maximal size of s-distance sets in various spaces has a long history in mathematics. We determine a new method of bounding th...