Strong Zauner conjecture for Weyl–Heisenberg SICs

For $d\geq1$, let a Weyl–Heisenberg SIC be a set of $d^2$ equiangular complex lines in $\C^d$ generated by a Weyl–Heisenberg fiducial vector. Strong Zauner Conjecture. For every dimension $d\geq1$, at least one Weyl–Heisenberg SIC exists. Explicit constructions prove this in many dimensions, including $d\leq53$, but the assertion is unresolved in general.