Uniform designs have been widely applied in engineering and sciences’ innovation. When a lot of quantitative factors are investigated with as few runs as possible, a supersaturated uniform design with good overall and projection uniformity is needed. By combining combinatorial methods and stochastic algorithms, such uniform designs with flexible numbers of columns are constructed in this article under the wrap-around \(L_2\)-discrepancy. Compared with the existing designs, the new designs and their two-dimensional projections not only have less aberration, but also have lower discrepancy. Furthermore, some novel theoretical results on the minimum-aberration, uniform and uniform projection designs are obtained.

统一设计已广泛应用于工程和科学的创新中。当使用尽可能少的运行研究大量定量因素时，就需要具有良好总体和投影均匀性的过饱和均匀设计。通过组合组合方法和随机算法，本文在环绕\（L_2 \）-差异下构造了这种具有灵活列数的统一设计。与现有设计相比，新设计及其二维投影不仅像差较小，而且差异也较小。此外，获得了关于最小像差，均匀和均匀投影设计的一些新颖的理论结果。