As someone with keen interest in physics (and a bit of training) I find speculation about "discrete space" disquieting. It's the level of abstraction where intuition about space breaks down, and you have to be very careful. Remember that coordinate systems are short-hand for measurement. It's one thing to admit fundamental limits on measurement resolution, and quite another to say that space itself is quantized! Mostly I get around this by not thinking about it; most of these theories are only testable in atrocious and unattainable conditions, doing things like performing delicate QED experiments at the edge of a black hole.

I don't think your "voxel" intuition can be right because it's a small jump from that to (re)introducing an absolute reference frame.