A leaked User Agent Profile seems to suggest that the LG G4 (or some other near-future LG flagship device) will come with an even higher resolution than we have been seeing with the 2K/QHD displays. A device with the model name LG-VS999 showed up in a leaked UAP, and it definitely shows a display with a 3K resolution, specifically, 1620 x 2880 pixels.
The VS in the name suggests this device is likely coming to Verizon since that's the way LG traditionally categorizes their device model names. If this device is the G4 and comes with the same 5.5-inch display, then the pixel density will be an insane 600ppi. Of course, at that size, you would need a magnifying glass to actually tell a difference between this display and any other flagship.
Of course, it would give LG marketing bragging rights... for whatever that's worth to consumers.
In case this is the LG G4... here's a link to our dedicated section for that device: LG G4 Android Forum at DroidForums.net
Source: LG 8217 s upcoming G4 could have a 3K display