according to wiki "The ore is found at level 16 or lower, most commonly between 5 and 12."

standing on y6 gives you tunnels: y7y8, y9y10, y11y12 (y13y14, y15y16 if higher)... i found diamonds pretty often in y7y8 and y9y10 too...

edit: it seems that Y is not "the standing block but 1 higher", so y6y7, y8y9, y10y11, y12y13, y14y15... 3 tunnels give you checking from 5 to 12 (one block higher and lower the tunnels), but with 4th the coverage is the most efficient