For the deadest room, you'll need more than only carpet but the thicker the better for starters. Use the thickest felt pad too. You'll also need to treat all walls, as thick as possible. If you have read the required reading, you'll know gapping +1 x absorber thickness (4 inches minimum) increases LF performance by 1 octave. Corner basstraps (12 each) are also required.
Correction: Regarding bass traps, I mean you have 12 corners in a rectangular room so you can locate bass traps in all 12 corners. As far as how many, that would depend one the length or each corner. The four wall to wall corners are often 8ft so that's eight 2x4ft panels right there. The other eight corners are wall to ceiling and wall to floor. You could fill the entire length or use fewer and spread them out. All this and much more is in the stickies at the top of the forum.