  We enumerate the low dimensional cells in the Voronoi cell complexes attached
to the modular groups $SL_N(Z)$ and $GL_N(Z)$ for $N=8,9,10,11$, using quotient
sublattices techniques for $N=8,9$ and linear programming methods for higher
dimensions. These enumerations allow us to compute some cohomology of these
groups and prove that $K_8(Z) = 0$. We deduce from it new knowledge on the
Kummer-Vandiver conjecture.
