Grow Box Exhaust Fan Setup
I'm going to have a 6 ft high by 6 ft wide by 3 ft deep grow box. I'm going to have the exhaust fan toward the top of the box. Do I need to make smaller holes at the bottom of the box so that my circulating fan in the grow box can get fresh air to the plants?
Answer: Your grow box will definitely need a source of fresh air. Making many smaller holes around the bottom of the grow box would create an entry point for this fresh air. As long as your grow box is relatively air tight (and your exhaust fan is powerful enough), running the exhaust fan should create negative air pressure inside the grow box....which should automatically pull fresh air into the box through the holes at the bottom of the box.
With many small air holes around the bottom of the box and powerful enough exhaust fan, the incoming "fresh air" may carry enough force to accomplish air circulation inside the box (around the plants) as well as taking care of air exhaust. Unfortunately, it takes a very powerful centrifugal fan or squirrel cage fan to produce that amount of air movement.
It is more likely that you will still need a small oscillating fan inside the box to stir the air around the plants, but you will have to make this decision for yourself once you get to that point. As long as you are getting a little leaf movement from every plant in the garden, you can consider the air circulation to be adequate (and you may not need the oscillating fan).
A couple things to keep in mind as you are building your grow box....the suggestions above will solve your "fresh air" question, but your biggest challenge will be controlling the temperature inside the box. For your fresh air source, you will need to use either cool air from outdoors or else an air conditioner. Also, when it comes time to flower your garden, the air intake holes may become a source of light contamination (with a little clever thought, this should be an easy enough problem to fix). I hope this helps you out, and Happy Growing!