I'm planning on installing 4" corrugated pipe to route water from the sump discharge pipe. How deep does this corrugated pipe need to be buried? I would think it does not matter, as long as the pitch away from the outlet is sufficient to route water away.
The key to any underground drain pipe is to also put it in a fabric sleeve made for the purpose to prevent it from eventually filling and clogging with dirt.
You also might consider ending the drain tile into a dry sump, such as a buried barrel filled with (broken) cinder blocks and bricks and covered with ground fabric for the same purpose.