What size is that tub?
I decked under my 8 person tub. I don't have my drawings handy but I seem to recall using 2x10's for beams, 2x8's for joists, 6x6 for posts. 12" spacing on the joists, 6' spacing on the beams with 5' spacing on the posts, 18" max overhang. 48" deep footings.
Make sure you notch the posts and block the joists.