Conjecture on equiangular lines saturating the relative and incoherence bounds

Let $\Omega$ be a set of equiangular lines in $\mathbf{R}^d$ that saturates the relative bound and incoherence bound.

Classification conjecture. Then $d=2,3,6,7,23$, and $\Omega$ is isometric to the corresponding example found in the examples section.

The conjecture proposes that the known examples exhaust the equiangular-line sets simultaneously attaining these bounds. It is presented after a theorem giving structural restrictions for such sets; the supplied text does not establish the classification.