Construction Of Sudoku Designs And Sudoku-Based Uniform Designs

Sudoku designs belong to U type design category in the experimental desings, almost all uniform designs were constructed on the basis of the sets of U type designs. Sudoku designs are special U type designs, there are necessary connections between Sudoku designs and uniform designs.Based on the above discussions, the dissertation is devoted to the following researches:(1) discussing a lower bound of m levels design in views of discrete discrepancy by using Lagrange multiplier and Taylor formula;(2) discussing the construction of Sudoku designs, giving the common algo-rithms of Sudoku designs and discussing their properties:(3) considering the construction of uniform designs in view of discrete discrep-ancy on the basis of constructed Sudoku designs by mirror mapping, discussing the relation of the squared discrete discrepancy between the constructed uniform designs and its sub-designs, between the constructed uniform designs and Sudoku designs.In the following, let us introduce the contents of each chapter in brief.Chapter 1 summarizes some related background of experimental de-sign and the innovation and structure of this dissertation.Chapter 2 briefly introduce some basic concepts, formulas that will be used in the other chapters.Chapter 3 briefly introduce a tight lower bound of m levels design in views of discrete discrepancy by using Lagrange multiplier and Taylor formula. The lower bound will provide a basis to discuss the properties and confirm the uniformity of Sudoku designs and Sudoku-based uniform designs in the Chapter 4 and the Chapter 5.Chapter 4 discusses the common algorithms of Sudoku design con-struction and their properties. This chapter mainly discusses Sudoku design particularity and regularity and gives the common algorithms of Sudoku design construction and discusses properties of Sudoku designs.Chapter 5 discusses the construction of uniform designs in view of discrete discrepancy on the basis of constructed Sudoku designs. This chapter mainly discusses the construction of uniform designs in view of discrete discrepancy on the basis of constructed Sudoku designs with the help of the mir-ror mapping method, gives theoretical proof and concrete examples. In addition, this chapter also discusses the relation of the squared their discrete discrepancy be-tween the constructed uniform designs and its sub-designs, between the constructed uniform designs and Sudoku designs.Chapter 6 summarizes the dissertation and prospects the future work.