On construction of equireplicated constant block-sum designs

Abstract

It is shown that in general, with arbitrary levels of quantitative treatment factor, the constant block-sum balanced incomplete block designs do not exist. I then provide, assuming it exists, a general approach to construct a constant block-sum equireplicated block design, possibly with unequally spaced treatments, from the incidence matrix of a block design with same parameters but without constant block-sum property. I illustrate the nuances of obtaining a solution or establishing its nonexistence via several examples of partially balanced incomplete block designs.

Keywords:

• Balanced incomplete block designs
• constant block-sum designs
• equireplicated block designs
• incidence matrix
• partially balanced incomplete block designs

Acknowledgments

I wish to thank all three referees and the associate editor for their helpful comments.