Otmar Ertl (@oertl) did a great job on HyperLogLog improvements in his article "New cardinality estimation algorithms for HyperLogLog sketches" https://arxiv.org/abs/1702.01284. Later he proposed to change Redis implementation of HyperLogLog (https://github.com/antirez/redis/pull/4749) and @antirez found that the new implementation is around 20% faster, simpler and has lower theoretical error.

We could improve ClickHouse uniqHLL12, uniqCombined aggregate functions and maybe introduce new function uniqHLL(q, p)(x) using same algorithm.