Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (6): 1802-1811.

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Lower Bounds for the Symmetric L2-Discrepancy of U-type Designs

Yiju Lei1(),Zujun Ou2,*()   

  1. 1 College of Mathematics and Statistics, Xinxiang University, Henan xinxiang 453003
    2 College of Mathematics and Statistics, Jishou University, Hunan Jishou 416000
  • Received:2021-07-22 Online:2022-12-26 Published:2022-12-16
  • Contact: Zujun Ou;
  • Supported by:
    the NSFC(11961027);the NSFC(12161040);the NSFC(11701213);the Natural Science Foundation of Hunan Province(2021JJ30550);the Natural Science Foundation of Hunan Province(2020JJ4497)


Uniform design is one of the main methods of fractional factorials, which has been widely used in industrial production, systems engineering, pharmacy and other natural sciences. Various discrepancies are used to measure the uniformity of fractional factorials, the key is to find an accurate lower bound of the discrepancy, because it can be used as a benchmark which measures uniformity of design. In this paper, the lower bounds for the symmetric L2-discrepancy on symmetrical U-type designs with four-level and asymmetrical U-type designs with two and three mixed levels and two and four mixed levels are abtained.

Key words: U-type design, Symmetric L2-discrepancy, Lower bound

CLC Number: 

  • O212.6