for the commonly used uniform distribution.
See: Entropy Coding Benchmark
Brotli's entropy encoder might be interesting for such comparison. A quick try on it gives 560795962 bytes (with -q 9). I suspect -q 11 will give 5-10 % more.
I got this result by removing the LZ77 and static dictionary part from the brotli encoder and the remaining code encodes at 40 MB/s (-q 9) and the result decoded at 110 MB/s. I suspect that one could get twice the speed by cutting it out more thoroughly.
Also, there is a dynamic block length dance going on. That is also somewhat limited at quality 9 and way more advanced at quality 10 and 11.