Let \(A\) be a finite subset of \(\mathbb{Z}^n\), which generates \(\mathbb{Z}^n\) additively. We provide a precise description of the \(N\)-fold sumsets \(NA\) for \(N\) sufficiently large, with some explicit bounds on ``sufficiently large." For example if \( A\) has exactly three elements we provide a precise description of \( NA\) for all \( N\geq 1\).