Ground size for 100 amp sub panel 200ft away

I would like to install a 120/240 volt 100 amp sub panel on a detached garage that is about 200 ft away. I have read that one should strive for a voltage drop of less than 3% and from what I can tell this means I need #2 cu or 1/0 al for the two hot and neutral. What I'm having a hard time determining is if the ground wire to the sub panel needs to be the same size or if it can be smaller. I've read that the ground for a 100 amp sub panel needs to be #8 cu or #6 al but don't I need to take the long distance into account?

I really appreciate any help on this!

Edit: Thank you Harper for pointing out that the 3% rule applies to expected loads, not the supply breaker size. Given my expected use I can probably go with slightly smaller wires for the two hot and nuetral. However I still have the same question about how to size the ground wire.

• The 3% target applies to the loads you actually expect, not the breaker trip value on the supply breaker. Right off the bat you should not plan to load the circuit beyond 80%. Jan 21, 2019 at 5:03
• Thank you Harper for pointing this out, I've edited my question to include this point. Jan 21, 2019 at 16:56