Minimally replicated PBIB designs for multi-environmental trials

Abstract

For situations in multi-site varietal trials where the experimenters demand incomplete blocks with unequal sizes, minimum number of replications, or both, new series of incomplete block designs have been presented. The proposed designs are higher associate partially balanced incomplete block designs in two replications having flexible block sizes. These designs are affine resolvable and are optimal in the competing class of resolvable incomplete block designs. The underlying association schemes of these designs are defined. Further, they can be advantageously used for obtaining designs for various stages of breeding trials. An R-package developed for generating these designs has also been demonstrated.

Keywords:

• Association schemes
• breeding experiments
• multi-site varietal trials
• optimal
• unequal block sizes

2020 Mathematics Subject Classification:

• 62K10

Acknowledgments

We are grateful to the editors and the reviewers for their constructive suggestions/comments that helped to improve the quality of the manuscript. First author is thankful to Post Graduate School, ICAR-Indian Agricultural Research Institute for the facilities received during the research.

Declaration of interest statement

There is no potential conflict of interest.

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.