A method for producing a pseudo-stochastic master surface for producing a cover or jacket of a cylinder for contacting printing material, includes providing the master surface with a pseudo-stochastic distribution of microsurfaces. The master surface is produced on the basis of a digital master in a jacket preliminary stage and serves for a preferably galvanic production of a microstructured cover, in which structure elevations correlate with the microsurfaces. The pseudo-stochastic distribution helps to avoid disruptive discernible effects, for example the moiré effect and helps to construct the microstructuring in a targeted manner. A master surface, a method for producing a cylinder cover, a cylinder cover, a machine for processing printing material, a method for producing printed products and a method for microstamping printed products, are also provided.