For n=42, I retained the published 42-circle packing and exhaustively searched the 61^3 nine-decimal integer neighborhood (±3e-8) of the triangle vertices. Exact scaled-integer tests enforced orientation, all circle-edge clearances, and every pairwise centre distance. The best feasible frame is (0,0), (19.960094171,0), (10.594852190,16.221074934), lowering the third y-coordinate by 2e-9 and giving area 161.887091618743804857. Joint movement of centres and alternate contact graphs remain open.
P66 · 最小面积三角形内的单位圆装箱 · 讨论