Projection uniformity of nearly balanced designs

The objective of this paper is to investigate the issue of the projection uniformity for nearly balanced designs under the wrap-around L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_2$$\end{document}-discrepancy. The projection uniformity criterion for nearly balanced designs defined, the projection uniformity of two- and three-level nearly balanced designs discussed. The lower bounds of the uniform projection measure of the nearly balanced design are provided, which can be used as a benchmark for searching optimal nearly balanced designs. Inspired by the construction of row augmented designs, the relationships of the uniform projection measure among the initial design, the added design and their combination are built, and the effective construction methods and algorithms of the nearly balanced designs are provided. Numerical examples are given to illustrate the constructed nearly balanced designs with high efficiency and good projection uniformity.