When generating a stream of random integral numbers lying within a certain interval (for simplicity let’s say those are bytes), I sometimes have a requirement (or at least a desire) to have the smallest possible deviation from a distribution (let’s say uniform distribution) for any arbitrary length of the stream.
In practice such stream should look like this:
$A = (\underbrace{a_1,\ a_2,\ \dots,\ a_{256},}_\text{[0, 255] placed in random order} \underbrace{a_{257},\ a_{258},\ \dots,\ a_{512},}_{\quad\text{[0, 255] placed in another random order}} \dots)$
Of course, this requirement is mutually exclusive with perfect entropy of the stream, because the probability of certain numbers appearing will slowly concentrate towards the 256th number, which will be the only possible one.
Anyway, the question is, how would you call it? I’m in no way a mathematician, but I’m sure that there is a name for such property of random streams.