The weak $d\times 2d$ equiangular tight frame conjecture

An equiangular tight frame (ETF) is a matrix with unit-norm columns, constant-modulus pairwise inner products, and frame operator proportional to the identity. The conjecture concerns complex matrices with $d$ rows and $2d$ columns.

Weak $d\times 2d$ conjecture. For every $d$, there exists a $d\times 2d$ ETF.

This conjecture was posed by Fallon and Iverson and is the weakest of the paper's hierarchy of existence claims. The source reports substantial partial progress, including verification of the broader all-dimensional claim through $d=165$ and numerical evidence through $d=1500$, but the universal statement remains open.