Even knowing the exact number of 1s and 0s buys you a few bits of information. log(201 choose 100) / log(2) = 196.843 Order the 201 choose 100 strings on 201

Even knowing the exact number of 1s and 0s buys you a few bits of information. log(201 choose 100) / log(2) = 196.843 Order the 201 choose 100 strings on 201 bits with exactly 100 0s lexicographically, write down the index in that list of your particular message in 197 bits in a completely ordinary fashion ;P. But to be clear, I don't disagree with what you mean at all.