The optimal resolution for the GearVR can be calculated:
The S6 and S7 have a resolution of 2560x1440, for one eye that results in 1280x1440 pixels.
The field of view on the Gear VR is approximately 90 degrees on S6 and close to 96 degrees on S7. If a FOV of 90 degrees has 1280 pixels, then 360 degrees has 4 (360/90) * 1280 pixels = 5120 pixels. If you'd use 1440 pixels (if FOV is measured vertically) this would result in 5760 pixels.
Because of the fact that GPU's can handle power of 2 image sizes the easiest, but 2048 would be overkill (memory use for 12 cubefaces with this size) and 1024 would be loss of quality, a size in the middle of 1024 and 2048 has been chosen: 1536x1536. Probably so a single texture of 1536x1536 can be constructed internally from one 1024x1024 image with five 512x512 images. This results in a horizontal size of 4x1536=6144 pixels, nicely above the needed 5760 pixels and without going overboard on pixels/memoryuse.