A flat product made of a metal material has been provided with deterministic surface texture which has a plurality of depressions which have a depth in the range of from 2 to 14 μm, wherein the depressions are designed to be I-shaped, H-shaped, cross-shaped, C-shaped or X-shaped, and wherein the surface texture has a peak count RPc in the range of from 45 to 180 1/cm, an arithmetic mean roughness Ra in the range of from 0.3 to 3.6 μm, and an arithmetic mean waviness Wsa in the range of from 0.05 to 0.65 μm. A roll which is particularly suitable for producing such a flat product has a deterministic surface texture which has a plurality of overlapping dimples, which are arranged such that they delimit a double-I-shaped, H-shaped, cross-shaped, C-shaped or X-shaped material texture in the roll surface, and wherein the surface texture of the roll, measured in the direction of the roll axis, is characterized by a peak count RPc in the range of from 80 to 180 1/cm, an arithmetic mean roughness Ra in the range of from 2.5 to 3.5 μm and an arithmetic mean waviness Wsa in the range of from 0.08 to 1.0 μm.