Engineered genetic systems are prone to failure when their genetic parts contain repetitive sequences. Designing many nonrepetitive genetic parts with desired functionalities remains a difficult challenge with high computational complexity. To overcome this challenge, we developed the Nonrepetitive Parts Calculator to rapidly generate thousands of highly nonrepetitive genetic parts from specified design constraints, including promoters, ribosome-binding sites and terminators. As a demonstration, we designed and experimentally characterized 4,350 nonrepetitive bacterial promoters with transcription rates that varied across a 820,000-fold range, and 1,722 highly nonrepetitive yeast promoters with transcription rates that varied across a 25,000-fold range. We applied machine learning to explain how specific interactions controlled the promoters' transcription rates. We also show that using nonrepetitive genetic parts substantially reduces homologous recombination, resulting in greater genetic stability.