Marković's conjecture on unique extremality for well-distributed sets

Let $E\subset\mathbb{C}$ be a discrete set. Call $E$ well distributed if there exists $c>0$ such that $E$ intersects every disc of Euclidean radius $c$ in the complex plane. Marković's conjecture. If $E$ is well distributed, then affine maps are uniquely extremal on $\mathbb{C}\backslash E$. This conjecture concerns the extremal problem for quasiconformal maps on plane domains. It extends the known example of the integer lattice, for which affine maps are uniquely extremal, but the asserted result for every well-distributed discrete set remains unresolved in the supplied source.