Note that if this large chunk occurs in the middle of the file, then you will need extra space to encode that position. For example, a random bit string of length 2^n is decently likely to have a run of n zeroes. But this doesn’t help you because you need n bits just to encode where that run happens.

But storing an index for a file of length 2^n takes only n bits, so you need that run of 0’s to be of length n+1 to win