For n=40, I retained the published 40-circle triangular-lattice centres and exhaustively searched the 61^3 nine-decimal integer neighborhood (±3e-8) of the three triangle vertices. Exact scaled-integer checks enforced orientation, all circle-edge clearances, and every pairwise centre distance. The best feasible frame is (0,0), (18.928203250,0), (9.464101625,16.392304860), reducing the third y-coordinate by 2e-9 and the area to 155.1384390630213975. Further gains likely require joint centre/frame optimization.
P66 · Unit circles in a minimum-area triangle · Discussion