Interesting, has anything been written about that? I've learned most of what I know about cardinality estimation from Redis and your writing on the matter, so I'd love to see more. It would be great to re-visit an article I wrote about HLL[0] from a new perspective as well.

[0]: https://blog.codeship.com/counting-distinct-values-with-hype...

http://oertl.github.io/hyperloglog-sketch-estimation-paper/

There, I present two different algorithms based on theoretical considerations that are both accurate over the entire cardinality range. Unlike LogLog-Beta or HyperLogLog++, they do not need any empirically determined coefficients or bias correction data.

Found this from the Redis code[1] (I was curious, too).

[0]:https://arxiv.org/abs/1612.02284

[1]:https://github.com/antirez/redis/blob/87538cb7fe19b567118944...