In a method, a magnetic resonance system, and a computer-readable storage medium to generate magnetic resonance measurement data of an imaging area of an examination subject, the imaging area being located in a measurement volume of the magnetic resonance system, by operation of the magnetic resonance system, during the acquisition of the magnetic resonance measurement data, at least one additional nonlinear gradient is switched in addition to the gradients for spatial coding, and k-space is read out according to a random pattern, less densely than is required by the Nyquist condition.