The corners of the Note 4 don't fit into the Gear VR headset, but if you're prepared to modify your brand new headset there is a hack. A five year old could do a neater job than this guy and a dremel would produce much better results than a side cutter, but this video shows what you need to do.
I just realized that this is the new version of the Gear VR headset and over on XDA they say the Note 4 fits in this one without chopping it up. Find out more here:http://forum.xda-developers.com/mobile-vr/gear-vr/99-gear-vr-note-4-t3255739
Edited on 11/15/2016 at 8:02 PM. Reason: