Diagonal designs

• 2026-08-28 [Refuted] The diagonal designs are codes 98, 140 and 266 with Z_F(level) = 3^level - 2 - the identity fails at level = 0 (sides 0 and -1) and holds for every level >= 1, and the list is short by one: of the C(9,3) = 84 three-corner subsets of the 3 x 3 digit square, four are diagonal through level = 6, {(0,1),(1,0),(2,2)} (266), {(0,1),(1,2),(2,0)} (98), {(0,2),(1,0),(2,1)} (140) and {(0,2),(1,1),(2,0)}, code 84 (the value 148 once quoted for it names {(0,2),(1,1),(2,1)}, not a permutation design); the three named codes hold to level = 11 with every pair checked for collinearity at level = 7. Witness: gasket-ray-machine.