When I read about famous lattices ($E_8$, Leech, ...) I always only see listed the norm of their shortest vectors. However, I am interested in the norm of the second shortest vectors (and if possible, also the norm of the $n$-shortest vectors).

I am not interested in computing these for arbitrary lattices, but I want to know of a reference that tabulates these norms for the most important lattices, or learn of a way to compute these norms from the other data usually given for such lattices.

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    $\begingroup$ The lattices you mentioned are integral lattices, so the norm of every vector is by definition an integer. The position of the nonzero coefficients of the lattice's theta series describe which integers appear as norms of vectors in the lattice. I don't know of a standard reference, but many of these theta series can be found in the OEIS website (e.g. E_8 and Leech). $\endgroup$ – pregunton Jul 12 at 12:57

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