Downfiring subs on carpet?

Hel-loo, subwoofers moving/vibrating = distortion. Put your hand on your sub as a real low note comes along. Ideally you should not feel anything but all of you will notice your sub vibrating to one degree or another. Geoffkait uses his sub for massages. 
Ideally you would mount your sub driver in a concrete wall. Some new designs like the Magico use two drivers firing 180 degrees from each other. This is called balanced force. These subs will not move at all and if the cabinets are stiff enough you will not feel anything while the sub is playing. The best way to keep most subs from vibrating is to couple them to a larger fixed mass, the floor. The best way to do this other than bolting the sub to the floor is with spikes. This would give Geoffkait an even better massage.

Three spikes please! Four can rock.

It is very important that the sub can not move or vibrate. It should be coupled to the floor as best as possible. Spikes are the best whether the sub is on carpet or not. Right into the floor no pads. 

Mapman is correct. 100Hz has a wavelength of 10 feet. The only way the carpet would effect the sound is by lowering the resonant frequency of the floor by adding weight but no stiffness. The trick with the floor is to get it's resonant frequency outside the range of the subwoofer. Concrete is the ultimate. You can get wood floors stiff enough by using larger laminated joists and doubling up on the plywood. Use construction adhesive on everything. What you put the woofer on makes absolutely no difference. My woofers are on concrete. If I play a 20 Hz test tone the whole house becomes a symphony of rattles. Fortunately music masks the rattles. Low frequency sound is very powerful. In terms of distortion the most important factor besides the driver itself is that the enclosure is stiff and very heavy. Ideally when you put your hand on the sub while playing you should feel nothing. No vibration at all. Having said all this you can negate most of these problems with room control as long as they don't boost any given frequency more than 5 dB or so. After that you start running out of power and digital headroom.