You have 1000 bottles of wine, of which two are poisoned. Your taste-tester rats must work non-adaptively: you first pick which subsets all the rats drink, and then you learn whether each rat died.
If you try to find the poisoned bottles using the fewest rats, you’re doing “Combinatorial Group Testing”. But with only 10 rats, that’s information-theoretically hopeless. Our goal instead is to discard as few bottles as possible and be sure the rest are safe to drink.
Using a superimposed code we can discard 92 bottles of wine. We introduce a generalization allowing more superposition ambiguity which gets us down to 80 bottles, and then explore highly symmetric non-uniform probability distributions over codes which bring us down to at worst 78 bottles. I hope the rats appreciate the effort.