[Doctor Stochastic]

That's why you only get an upper bound. Perhaps lower perhaps not. As these numbers all obey the "strong law of large numbers" they all have about the same behavior. The strong law (in this case) says that all bit sequences will appear with the proper frequency. That is half 1's, half 0's, a quarter each of 00,01,10,11, etc.

[Alamo-Girl]

Thanks for the information! I had read that Champernowne's constant is known for that in base ten, but not determined in other bases. Are there new determinations?