Let $A$ be an abelian surface and $\text{Km}(A)$ be the Kummer surface of $A$. If I remember correctly, the Picard number $\rho(\text{Km}(A))$ is equal to $16+\rho(A)$. 



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The Picard number of the Kummer surface of an abelian surface
In the fourth section of this paper <http://www.staff.uni-bayreuth.de/~bt270951/quart9h.pdf> they sketch the proof. 


The idea is that the orthogonal complement of the subspace generated by the sixteen $-2$ curves in $\mathrm{H}^2(Km(A),\mathbb{Z})$ is isomorphic to $\mathrm{H}^2(A,\mathbb{Z})$.


