From the datasheet for the ATmega640/1280/1281/2560/2561
In the details for the 100C1 CBGA:
Ball diameter: Min: 0.35mm (13.78 mil) Typ: 0.40mm (15.75 mil) Max: 0.45mm (17.72 mil)
It doesn't actually give a recommended landing pattern as such, unfortunately, like a lot of other data sheets do, so it's pretty much guesswork what the size should be.
16 mil is a good size as it's pretty much the "typical" ball size. 14 mil would be acceptable I guess at a pinch.
I wouldn't go below 14 mil - that's just asking for trouble.
16 mil is exactly what DipTrace provides on that pattern so they agree with you. I guess I will try again with 14 mil pads and see what I can get it to do.