related and useful: "Ribbon filter: Practically smaller than Bloom and Xor" (https://arxiv.org/abs/2103.02515)
This paper does a good job of showing the space/time tradeoffs of various approximate sets.
This paper does a good job of showing the space/time tradeoffs of various approximate sets.
The paper includes comparisons with Ribbon filter
[1] Graf, T. M., & Lemire, D. (2022). Binary Fuse Filters: Fast and Smaller Than Xor Filters. arXiv. https://doi.org/10.1145/3510449
If you're willing to compare arbitrary operating behavior, a simple entropy coded bitset will achieve the information theoretic bound -- it just isn't updatable or queryable on the fly. :P