# Probability: What is the minimum expected distance from Hamming?

If i try $$N$$ binary length chains $$n$$ evenly and independently, in principle I can find the closest Hamming distance between any pair. What is the expected value for this minimum?

If this is difficult to calculate exactly, is it possible to give a good approximation for large $$N gg n$$?

I see this question closely related but with $$N = n$$.