Universally optimal balanced block designs for interference model

The interference model has been widely used and studied in block designs where the treatment in a particular plot effects on ones in its neighbor plots. There are many experiments specially in agricultre that block size (k) is greater than the number of treatment (t). If k>t\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k>t$$\end{document}, the universally optimal designs under the interference models are usually difficult to obtain. In this paper, we consider an interference model with equal left- and right-neighbor effects for uncorrelated errors when k>t\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k>t$$\end{document}. Based on Kushner’s method, we obtain the universally optimal designs on the class of circular block designs. We also present some methods to construct these designs. Then, we generalize our results for one-sided interference models.