Samsung Display developed a new high-resolution OLED display, specifically for VR applications. The 5.5" panel, on display at SID DisplayWeek, sported a 3840x2160 resolution - or 806 PPI. The panel offered a brightness of 350 nits and a color gamut of 97% adobe RGB.
This is the highest resolution mobile phone sized OLED ever demonstrated, and it exactly matches the highest resolution LCD - Sharp's 5.5" 806 PPI IGZO panel unveiled in 2015. Samsung's display probably uses some sort of PenTile architecture, though, so actual sub-pixel count is smaller.