English

More on the optimal arrangement of $2d$ lines in $\mathbb{C}^d$

Metric Geometry 2024-10-24 v1 Combinatorics Functional Analysis

Abstract

We introduce a new infinite family of d×2dd\times 2d equiangular tight frames. Many matrices in this family consist of two d×dd\times d circulant blocks. We conjecture that such equiangular tight frames exist for every dd. We show that our conjecture holds for d165d\leq 165 by a computer-assisted application of a Newton-Kantorovich theorem. In addition, we supply numerical constructions that corroborate our conjecture for d1500d\leq 1500.

Keywords

Cite

@article{arxiv.2410.17379,
  title  = {More on the optimal arrangement of $2d$ lines in $\mathbb{C}^d$},
  author = {Joseph W. Iverson and John Jasper and Dustin G. Mixon},
  journal= {arXiv preprint arXiv:2410.17379},
  year   = {2024}
}