Actually, you can have images with up to (2^32-1)(2^32-1) pixels.
Given each pixel stores 64 Bits of data, there are 2^64 combinations for each pixel, yielding in the total number of possible images as:
(2^64)^((2^32-1)(2^32-1)) ~ 10^(10^21)
I meant 2R,2G,2B,2A images, i.e. 8 bit per pixel. That was my misreading - it is actually 2 bytes per channel, (I'm used to image color depths being quoted in bits.) I need to read more carefully, sorry.
2222 images?
The color depth, 8 bit per pixel, with 2 bit per channel. But that was my misreading, it is 64 bits per pixel. So not 'too limited' at all.