In the study, we introduce a new technique, sparse spectrum with uniform wave vectors (SU), for generation of phase screen samples. In a manner similar to the known sparse spectrum (SS) technique, it uses a trigonometric series with random discrete spectral support. However, in contrast to the SS technique, random wave vectors are uniformly distributed on individual segments of the wave vector plane partition in the SU technique. We compare the accuracy and computational effectiveness of the SU technique with the subharmonics complemented discrete Fourier transform (DFT) technique, SS technique, and randomized DFT technique [ J. Opt. Soc. Am. B36, 3249 (2019)JOBPDE0740-322410.1364/JOSAB.36.003249]. The SU and SS techniques generate unbiased samples and indicate superior computational effectiveness for 1 MP and larger screens.