Hardness radius of Dominating Set under maximum-degree distance

Determine the hardness radius of Dominating Set under the maximum-degree distance, where the distance between two graphs on the same vertex set is the maximum degree of their symmetric difference.

Background

The paper gives a lower bound of n^{1-o(1)} for the hardness radius of Dominating Set under the maximum-degree distance and an upper bound of n/e for the tractability radius. The precise radius, and potentially the gap between the known lower and upper bounds, is not determined.