Can you make a simulation of this idea - see https://theconversation.com/the-maths-logic-that-could-help-test-more-people-for-coronavirus-134287 - in Snap! ?
I find comments under the article an interesting read, too.
This isn't really relevant to the problem, but something that jumped out at me was the "b ≠ c ≠ d" above the chart. The ≠ relation isn't transitive; from this information we don't know whether or not b = d. (By contrast, = is transitive, so from "R₃ = R₄ = c" we do know that R₃ = c.) I expect they meant that no two of b, c, and d are equal, but they didn't quite manage to say it.
Do I understand correctly that (("b ≠ c") AND ("b ≠ d") AND ("c ≠ d")) is what author has in mind, however the notation "b ≠ c ≠ d" is not good?
5 + 2 ≠ 6 ≠ 7
I honestly wish I could try to make this, but both approaches in the paper are poorly explained. In the first approach, the author (Kadri) defines l but it's never used or even mentioned in the actual procedure, among other problems. And in approach 2, there's a step function that is said to determine whether or not to add a patient's samples to a cup, but how exactly this is determined is undefined. Maybe it's just arbitrary, but maybe it's not, because a patient's samples can only be added to half of all the cups, no more, no less (and it must be unique, to place further constraint).
I think there needs to be some sort of formal definition. I don't know, maybe I'm an idiot or something, but there's way too much in the air for me to know how exactly the program should work.
At least you understand what is missing in the article, which is more than I do. If you are an idiot than I am super-idiot. If you really wish to do it, however, maybe you can send an email and ask him to fill the missing info in his article kadriu@cardiff.ac.uk (I think he would be glad that someone really took an effort to understand his idea, what do you think?)