The answers here didn't really address what I was looking for (How many bits are needed to simulate the universe?), so...
If we are in a simulation, can we presume the simulation only needs to be perfect at the levels at which we consciously observe it, and it can therefore become more and more 'fuzzy' as we 'zoom out' (ie, we don't need to simulate all the atoms on the moon etc)? If so, in order to make the simulation just good enough to pass all our tests, only a fraction of the bit space for simulating the whole universe would be needed, and there must be plenty of opportunities for data compression too.
In other words, to create a simulation of the universe as "we observe it", how much storage is likely to be required?