On classifying Minkowskian sublattices

Let Λ be a lattice in an n-dimensional Euclidean space E and let Λ′ be a Minkowskian sublattice of Λ, that is, a sublattice having a basis made of representatives for the Minkowski successive minima of Λ. We extend the classification of possible Z/dZ-codes of the quotients Λ/Λ′ to dimension 9, where dZ is the annihilator of Λ/Λ′.