If you enjoyed XOR filters, you might also like ribbon filters, something that I had the pleasure of working on last year. They share the basic idea of using a system of linear equations, but instead of considering 3 random positions per key, the positions to probe are narrowly concentrated along a ribbon with a typical width of 64. This makes them far more cache-efficient to construct and query.

By purposefully overloading the data structure by a few per cent and bumping those items that cannot be inserted as a result of this overloading to the next layer (making this a recursive data structure), we can achieve almost arbitrarily small space overheads: <1% is no problem for the fast configurations, and <0.1% overhead with around 50% extra runtime cost. This compares to around 10% for XOR filters and ≥ 44% for Bloom filters.

In fact, I'm going to present them at a conference on Monday - the paper is already out: https://drops.dagstuhl.de/opus/volltexte/2022/16538/pdf/LIPI... and the implementation is at https://github.com/lorenzhs/BuRR/. I hope this isn't too much self-promotion for HN, but I'm super hyped about this :)