Does a sub need to be on the floor?

Short answer, the best position for a sub is how it loads the particular room it’s in. I have done experiments with raising and lowering a REL Strata lll in the front corner and the best position for bass articulation, extension and soundstaging was positioned in the middle with the driver facing the ceiling. I used the Strata lll as it is easy to move around and lift but the results speak for themselves.

Of course, this looks very odd and also needs a solid platform to perform best but it did teach me about how subs load a room. My current sub which is a REL Stadium lll works best sitting in the front corner, driver facing down with port positioned outward. I tried it with the driver facing the ceiling and the port positioned next to the wall and the results were impressive with regards to extension but integration with the main speakers was problematic.

It always pays to play with positioning in one’s own system despite what conventional wisdom dictates.

/erik_squires im liking you more and more reading your post .. 
I'm by no means a headphone fan but sometimes choosing the lesser of two evils may be key . 
     Inna same to you i think we are on the same path in our thought path

   Op . I would personally hesitate putting a sub somewhere that is not somewhat stable it will resinate and you will battle that demon imo .. Put the sub on a worthy platform or audiopoint or stillpoints but all these seem bassackwards get a good pair of spkrs buddy start there subs come later imo .. 
Respect 

Is there any wall mounts for subs?

wolfernyc

Well designed subs are usually designed/voiced to go on the floor and to get loading from it by the manufacturers.
  
If raised off the floor, you may "think" it's tighter, but in fact your losing bass extension/loading.

If your worried about your neighbors, put a big a cement paving slab under the sub, they're cheap come in different sizes and you can paint them.  

Cheers George

I think there is another thread on Audiogon discussing putting subs on stands. It was a couple of months ago. If I remember correctly, some said it made the subs sound better.