  A simple sextic is a reduced complex projective plane curve of degree 6 with
only simple singularities. We introduce a notion of Z-splitting curves for the
double covering of the projective plane branching along a simple sextic, and
investigate lattice Zariski k-ples of simple sextics by Z-splitting curves. We
define specialization of lattice types, and classify all lattice types of
Z-splitting curves of degree less than or equal to 3 up to specializations.
