Regarding the footprint of a 400w lamp, there are some calculations to keep in mind - particularly lumens/sq ft. The sun is approx 10,000 lumens per sq ft, so that's what would be considered optimal. You can do ok with as low as 5000 lumens per sq ft, but it's not optimal.
A 400w hps produces approx 50,000 lumens. To get optimal lighting (10,000 lumens/sq ft) you could only light 5 sq feet, which is 2.5 feet x 2 feet. If you go with minimal lighting (@ 5000 lumens/ sq ft) you could cover 10 sq ft, which is just slightly over 3' x 3' -- and again that's minimal lighting. Hopefully now you can understand why a 4x4 is too much space for a 400w.