Seems to me that as long as the total number of bits is the same it makes no difference whether each hash function has a separate table or not.

EDIT: Although, https://chatgpt.com/share/6a67336b-8600-83ed-9671-fab769b485... - it is in fact ever so slightly less effective if you have a separate table for each hash function

EDIT2: In the limit, if the number of hash functions equals the number of bits, then we can see that inserting one element would set all bits in the case where we use separate tables, but only 50% of bits if they use one big shared table.

So the false positive rate is higher if they use separate tables.

Assuming independent hash functions, giving each hash function it’s own bit table is equivalent to having one bit table with a number of bits equal to that of the sum of the numbers of bits in each hash function.

It would be more effective in avoiding false positives, but require more (typically a lot more) space.