A Power-Diagram Upper Bound for Twenty-Six Variable-Radius Disks in a Square

Let $S_{26}$ denote the supremum of the sum of the radii of 26 pairwise interior-disjoint closed disks of positive radius contained in the unit square. We prove $2.635983084917607783\ldots \le S_{26}\le \sqrt{\frac{2577}{2500}+\frac{11}{\sqrt3}}=2.716919756099889566\ldots$. The lower bound is accomp