400w HPS

what would be the smallest grow closet/box i could have in theory with a 400w HPS

Whatever you can fit the ballast in, provided it's got enough airflow not to burn the plants. Those things put off some heat.

as a rule of thump a 400W cover about 3x3 ft

and I must agree, heat will be your biggest enemy with a HID in a small box, so make sure you invest in a good ventilation and IMO a cool tube

I currently run a 400w HPS in a .5 x .9 x 1.6m tent, and it can get out of hand in there. I gotta make sure im on top of the ambient temp in the room. And even with that, I cant run in the heat of summer. Just too hot without air con. And on top of all that, Ive got a cooltube. So get a cooltube at the very least.