We characterize reflectable bases for affine reflection systems (extended affine root systems) of types This completes the characterization of reflectable bases for reduced affine reflections systems. We prove that a subset of non-isotropic roots is a reflectable base if and only if it is a minimal generating set for the root lattice. Our approach also provides a new less involved proof for simply laced types different from Using our characterization, we enumerate reflectable bases for the finite type E 6.