Is there any upper limit for the period of any pseudo-random number generating algorithm with a fixed number of bits? I know there are some algorithms with a very large period, such as MT19937, but I wonder if it is possible to derive a theoretical maximum period for any given bit length.
Edit:
As pointed out in the comments, this is not so much about the number of output bits as about the total number of bits that the algorithm can use to store a state.