Algebraic varieties over function fields and good towers of curves over finite fields

Given a smooth algebraic variety over a function field we can construct a tower of algebraic curves (or, equivalently, a tower of function fields). We say that the tower is good if the limit of the number of points on a curve divided by genus is positive. For example, the generic fiber of the Legendre family of elliptic curves gives a good (and optimal) tower over $\mathbb{F}_{p^2}$. I will speak on good towers coming from K3 surfaces.