  A generalized Kummer surface $X=Km(T,G)$ is the resolution of a quotient of a
torus $T$ by a finite group of symplectic automorphisms $G$. We complete the
classification of generalized Kummer surfaces by studying the two last groups
which have not been yet studied. For these surfaces, we compute the associated
Kummer lattice $K_{G}$, which is the minimal primitive sub-lattice containing
the exceptional curves of the resolution $X\to T/G$.
  We then prove that a K3 surface is a generalised Kummer surface of type
$Km(T,G)$ if and only if its N\'eron-Severi group contains $K_{G}$.
  For smooth-orbifold surfaces $\mathcal{X}$ of Kodaira dimension $\geq 0$,
Kobayashi proved the orbifold Bogomolov Miyaoka Yau inequality
$c_{1}^{2}(\mathcal{X})\leq3c_{2}(\mathcal{X}).$ For Kodaira dimension $2$, the
case of equality is characterised as $\mathcal{X}$ being uniformized by the
complex $2$-ball $\mathbb{B}_{2}$. For smooth-orbifold K3 and Enriques surfaces
we characterize the case of equality as being uniformized by $\mathbb{C}^{2}$.
