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

Lattice Zariski k-ples of plane sextic curves and Z-splitting curves for double plane sextics