There was a study, IIRC from Israel, which said this is still reliable with 64 samples mixed.
The next question is, do you need to test the individual samples then? Not sure how much available material for testing you have, but you might be able to just divide the mix to eliminate bigger groups first.
Or even mix parts with new samples. There must be an ideal procedure (throughput-wise) if you know how the range of positives to expect.
Note that optimal branch factor would probably depend on the expected negative rate. If 98% of your samples are coming back negative, it may be more optimal to divide by into 4 or 8 groups instead of 2 groups.
If the initial test size is 64 and contains a positive, split into two groups of 32 and test each. Continue splitting and testing when a positive is encountered.
It's only tenfold if they all test negative, right? Otherwise you need to test subgroups to find out which test(s) were positive. So the real speedup is probably something like 2x-4x, depending on infection rates.
Currently in the US ~85% of tests turn negative. If sample turned positive you'd perform 10% more tests (1 extra test for each 10 tests) i.e. x1.1. If it turned negative you'd perform 10% the tests you'd normally perform without this scheme i.e. x0.1. In this case .85 of tests would be .1 of what they're now. The rest of .15 will be 1.1 of what they're now. So if US did this, they would be testing ~x.3 of their current testing. This seems huge. Can someone check my math please.
This isn't accounting for combinatorial math. If each sample is negative 85%, then the probability that all 10 samples are negative is 0.85^10, or about 20%. If any sample turned positive (the other 80% of the time), then all will need to be retested. Instead of 1 test per sample, you're now running 0.2 * 0.1 + 0.8 * 1.1, or about 0.9 tests per sample. You've increased throughput by 10%, but not nearly as much as was hoped. Note that these numbers get more favorable with more negative tests, though.
The general formula is (r^x) * (1/x) + (1 - r^x) * (1 + 1/x), where r is the percentage of negative tests and x is the number to mix.
With an 85% negative rate, it's more beneficial to mix 3 tests at a time for 0.72 tests per sample. (2 samples gives 0.78 tests, 4 gives 0.73) As more samples come back negative it becomes more advantageous to mix more, but you shouldn't mix 10 tests at a time (as opposed to 9) till you get to about a 96% negative rate, at which point you're running 0.44 tests per sample.
Edit: The binary search algorithm mentioned elsewhere would probably be more optimal, but I'm gonna do my day job instead of figuring out the dynamics of that one.
What if you consider external factors too? You can have a simple survey asking whether they have been traveled recently, whether they have symptoms, whether they are essential workers, if they know somebody that was infected, where they are living, with how many people, etc... You can easily use theses answers to remove the ones most likely to test postive with theses answers.
If you include that your goal is to test everyone too, I have no doubt that you can easily reach 96% negative test quite easily.
I remember in Quebec while we were only testing people with symptoms and that had traveled (or have been in contact with someone that has been tested positive), we were still way higher than 90% of negative tests (even right now we are a 90.1%
The next question is, do you need to test the individual samples then? Not sure how much available material for testing you have, but you might be able to just divide the mix to eliminate bigger groups first.
Or even mix parts with new samples. There must be an ideal procedure (throughput-wise) if you know how the range of positives to expect.