Tables of the existence of equiangular tight frames

Abstract

A Grassmannian frame is a collection of unit vectors which are optimally incoherent. To date, the vast majority of explicit Grassmannian frames are equiangular tight frames (ETFs). This paper surveys every known construction of ETFs and tabulates existence for sufficiently small dimensions.

References in corpus (1)

• On the rigidity of geometric and spectral properties of Grassmannian frames

Cited by in corpus (17)

• Dimension towers of SICs. I. Aligned SICs and embedded tight frames
• Neural Collapse Under MSE Loss: Proximity to and Dynamics on the Central Path
• Equiangular tight frames and unistochastic matrices
• On the rigidity of geometric and spectral properties of Grassmannian frames
• New Constructions and Characterizations of Flat and Almost Flat Grassmannian Fusion Frames
• Quantum measurements with prescribed symmetry
• Constructions of biangular tight frames and their relationships with equiangular tight frames
• A Gramian Description of the Degree 4 Generalized Elliptope
• Certifying the novelty of equichordal tight fusion frames
• Six constructions of asymptotically optimal codebooks via the character sums
• Constructions and properties of optimally spread subspace packings via symmetric and affine block designs and mutually unbiased bases
• Geometric properties of SIC-POVM tensor square
• Low frame coherence via zero-mean tensor embeddings
• Infinite families of optimal systems of biangular lines related to representations of $\text{SL}(2,{\mathbb{F}}_q)$
• Asymptotically optimal codebooks derived from generalised bent functions
• Learning overcomplete, low coherence dictionaries with linear inference
• On the Search for Tight Frames of Low Coherence