[oertl]

If you are interested in new cardinality estimation algorithms for HyperLogLog sketches you could also have a look on the paper I am currently working on:

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.