Structurally Incomplete Row–Column Designs

Abstract

This article studies the optimality and construction aspects of structurally incomplete row–column designs in which the number of non-empty nodes in rows and/or columns are unequal. Universal optimality of structurally incomplete row-column designs with unequal row and/or column sizes has been investigated. General methods of construction of universally optimal designs are obtained using pairwise balanced block designs and block designs with nested rows and columns. One method of construction gives SIRC design with equal row and equal column sizes. A method of construction of structurally incomplete row–column designs for comparing test treatments with control treatment(s) is also given.

Keywords:

• Structural balance
• Extended structural balance
• Universal optimality
• Pairwise balanced block design
• Block designs with nested rows and columns
• Row-regular generalized Youden designs
• Balanced bipartite block designs

Acknowledgments

The authors are grateful to the referees for making valuable suggestions that have led to a considerable improvement in the earlier version of the manuscript.