To see that Alon’s Proof On The Lower Bound on F∞ works for sequences of length greater than 2n as well.

Simply consider that for characteristic vectors x,y instead of having lengths x + y have lengths m/n x + m/n y

And the sequence A of this length is as follows. For every member of subset of N for which x is a characteristic vector, put that member m/n times in the sequence.

Now the rest of the procedure follows except that the second party outputs “disjoint” or 0 if the output of the approximation algorithm is less than 4/3 (m/n) and 1 otherwise. This is the correct value with probability at least 1 – є because the precise value of F∞ is m/n if the sets are disjoint and 2m/n otherwise.