Construction of Row-Column Designs from a Class of Nested Balanced Incomplete Block Designs

Designs that possess the ability to remove heterogeneity in the experimental material, have received considerable attention in the literature. By convention, the parameters of row-column designs constructed in this paper are v,b,p,q which respectively denote the number of treatments, rectangular blocks, rows and columns; and indeed, each of the rectangular blocks has nested within it, p rows and q columns. Designs of series I and II which are block designs are re-configured in a systematic manner in this paper to give block designs with the ability to remove heterogeneity in multiple directions, namely row and column; and these row and column are also nested within each of available rectangular blocks. All the designs constructed are balanced with respect to two of the three components of the resulting designs namely, rectangular block and, column. This is consequently reflected in the concurrence of treatment pairs that were obtained for the row (λijr), column (λijc), and rectangular block (λijb) components of the designs respectively.