Denote by $\mu_n$ the largest value such that there exists a lattice of determinant $1$ in $\mathbb R^n$ for which the distances between different lattice points are greater or equal to $\mu_n$.
Korkine, Zolotareff, and then Blichfeldt found $\mu_n$ for $n=2,\ldots , 8$ (cf. H.F. Blichfeldt, The minimum value of positive quadratic forms in six, seven, and eight variables. Math. Z. 39 (1935), 1-15).
What about $n>8$?