The sampling theorem tells us that a signal with no frequencies above $f$ can be completely described by sampling it a rate of $2f$. However, the theorem makes no reference to quantization, and so I would think that the result only holds for samples measured with infinite precision.
However, in DSP we never have infinite precision, we instead have a fixed (or at least bounded) bit-depth. So what is the relationship between the bit-depth of each sample and the precision with which we could reconstruct the original signal? Does grossly over-sampling allow us to heavily quantize each sample?
For the purposes of the question, we could even imagine taking countably infinite samples from a signal that is infinite in the time domain, but each sample is itself limited to a resolution of $n$ bits.