Representations of codimension \(\geq 3\) by definite quadratic forms (Q1271160)

Let \(M\) be a positive definite quadratic \(\mathbb{Z}\)-lattice of rank \(\geq n+3\). If \(N\) is a quadratic \(\mathbb{Z}\)-lattice of rank \(n\) which is primitively represented by the genus of \(M\) and if all the successive minima of \(N\) increase sufficiently quickly, then there exists a global primitive representation of \(N\) by \(M\) with approximation and primitivity properties.