Affine-plane ideal-solution-clutter conjecture

Let ${\mathscr C}$ be a clutter of a combinatorial affine plane, and suppose that its blocking number is at least $3$. An ideal solution clutter is an ideal clutter associated with a solution of the relevant clutter problem. Affine-plane conjecture. A clutter of a combinatorial affine plane of blocking number at least $3$ has no ideal solution clutter. The source says this conjecture implies the cited conjecture about combinatorial projective planes other than $F_7$, which is described there as a famous open question; no resolution of the affine-plane conjecture is supplied.