@Jennifer Did you look into extreme value theory books?

@Felipe I am not a topologist. So I am asking this question. Is there a connection between $n$-tori and codes of length $n$ over $\mathbb{Z}/q$?

@Felipe After reading through some portions(of what I understand) of the paper "Euclidean weights of codes from elliptic curves over rings" by yourself and Judy walker, there seems to be a straight forward connection between euclidean and lee distance. It is well known euclidean distances is connected to lattice codes or shells of lattice codes. If we know bounds on densities of lattices would that not provide some kind of hint to lee distance bounds for odd alphabets? I may be mistaken. But your response is very welcome. Thankyou:)!!!!

@Felipe I forgot the alphabet constraint. Let me add that as well.

@Victor what is gp?