Test random overlapping groups, then logically deduce who isn’t infected and who how probably is. Tune group size and test count using simulations on generated data. I intuit that serial tests gain little unless P is << 1⁄64. In that case, test non-overlapping groups, then run the non-serial protocol on everyone who was in a yes-group—within those, we can update P to >= 1⁄64.
Test random overlapping groups, then logically deduce who isn’t infected and who how probably is. Tune group size and test count using simulations on generated data. I intuit that serial tests gain little unless P is << 1⁄64. In that case, test non-overlapping groups, then run the non-serial protocol on everyone who was in a yes-group—within those, we can update P to >= 1⁄64.