Suppose we have 2 pigs, 15 mins to die, 60 mins to test.
Then we can test 4 rounds.
But what is the maximum groups we can test in a round??
Remember the Venn diagram, we can have 4 possible situations.
That is, we can test 4 groups with this 2 pigs, we give the example in the following:
A B C D pig1 pig1 pig2 pig2
we can let pig1 drink the water from group B and group C,
and pig2 drink the water from group C and group D.
With this property, we can test 4^4 = 64 buckets in the end.
How about we have x pigs and d mins to die, t mins to test??
We can test 2^x groups in a round, and we have $ r = int(t / d) $ rounds.
So, we can test at most (2^x)^r buckets.
p.s. I suppose a pig can drink lots of water, lol.