Well, it took a global pandemic, but we finally found a use for bloom filters!
What is surprising is that group testing tells us that we can actually do better: the specific construction you pinpoint the people who come up positive, without needing to have a test for each person [1] and this result is optimal in the expected number of tests. I'm surprised that most labs haven't already been doing this (but I would suspect some have).
Wootters has wonderful notes on the mathematical background for this—I really recommend them. [2]
-----
[0] https://en.wikipedia.org/wiki/Group_testing
[1] Of course, we require an upper bound on the total prevalence, but even a weak upper bound yields fairly good savings in testing.
[2] Page 3 on of http://web.stanford.edu/~marykw/classes/CS250_W18/lectureNot...
> the specific construction lets you pinpoint the people who come up positive
A bottle neck seems to be that it's not really possible to pool more than at most 32 patients at a time.
It's an early work in progress but have a look: https://www.pcr-pooling.com
I have a link on my notes below. I'll add your site to the reference list at the top tonight.