I wouldn't worry about the "noise floor"-thing unless a pitch black background for ALL headphones is one of your key requirements, and it would be my guess that the list of amps to choose from wouldn't be very big.
I can hear a faint noise floor in the DT770's (80ohm/96db) when there is no music playing or there is a pause in the music, but it does not get higher when the volume is turned up. It is higher, and uncomfortably so, with the FA-002W (64ohm/105db) and IEM's (Dunu DN-2000 16ohm/102db), but the amp is clearly not designed with these in mind. I would expect it to be dead silent with less efficient headphones.
As far as efficient planar headphones go, I have no first hand experience yet. However Mike Mercer has been very positive about his experience with this amp and the open back Audeze EL-8 in another thread. For example:
http://www.head-fi.org/t/749214/audeze-el-8-the-el-8-is-a-must-hear-at-ces-2015/2700#post_11354436
http://www.head-fi.org/t/749214/audeze-el-8-the-el-8-is-a-must-hear-at-ces-2015/2715#post_11356084
Would love to hear from anybody using Fostex TH 900 with this amp..?
I want to understand the floor noise. So when there is no music is playing there is a slight noise which doesn't increase with increasing the volume, right?
My question, can I say that while playing the music the floor noise is still there but we don't hear it due to the presence of frequencies from the music? If yes, I assume this affects the fidelity of the music due to the presence of extra frequencies at the background.