2018/01/14 by Yen-chi Roger Lin, Lin, Yen-chi Roger, Wei-Hsuan Yu +1
Computer Science · Mathematics · #05C50 #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Mathematics and Applications #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.1801.04502
openalex publication_date 2018/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A set of lines through the origin in Euclidean space is called equiangular when any pair of lines from the set intersects with each other at a common angle. We study the maximum size of equiangular lines in Euclidean space and use graph theoretic approach to prove that all the currently known construction for maximum equiangular lines in \mathbb Rd cannot add another line to form a larger equiangular set of lines if 14 ≤ d ≤ 20 and d ≠ 15. We give new constructions of large equiangular lines which are 248 equiangular lines in \mathbb R42, 200 equiangular lines in ℝ41, 168 equiangular lines in ℝ40, 152 equiangular lines in \mathbb R39 with angle 1/7, and 56 equiangular lines in \mathbb R18 with angle 1/5.