In order to execute a low-artifact magnetic resonance fingerprinting (MRF) scan, a preferred order of N k-space trajectories of a sampling pattern is determined in a computer, along which in each case an undersampled scan data set is to be scanned, such that artifacts are avoided in parameter maps created from the scan data sets in an MRF scan. The order in which the N k-space trajectories are to be sampled one after the other is varied, so at least two different orders are produced. According to the orders that result due to this variation, determined test signal characteristics are compared with each other and/or with ideal signal characteristics with respect to their artifact behavior. A preferred order is determined from the resulting orders by taking into account the results of the comparison.