Though the Bloom filter is a textbook algorithm, it has some significant downsides. A major one is that it needs many data accesses and many hash values to check that an object is part of the set. In short, it is not optimally fast.
Can you do better? Yes. Among other alternatives, Fan et al. introduced Cuckoo filters which use less space and are faster than Bloom filters. While implementing a Bloom filter is a relatively simple exercise, Cuckoo filters require a bit more engineering.
Could we do even better while limiting the code to something you can hold in your head?
It turns out that you can with xor filters. We just published a paper called Xor Filters: Faster and Smaller Than Bloom and Cuckoo Filters that will appear in the Journal of Experimental Algorithmics.