On projections of arbitrary lattices

In this paper we prove that given any two point lattices Λ1⊂Rn and Λ2⊂Rn−k, there is a set of k vectors {v1,…,vk}⊂Λ1 such that Λ2 is, up to similarity, arbitrarily close to the projection of Λ1 onto the orthogonal complement of the subspace spanned by {v1,…,vk}. This result extends the main theorem of Sloane et al. (2011) [1] and has applications in communication theory.