Constant block-sum Youden-m square and PBIB designs using Galois field

Abstract

In the present paper, we have discussed the construction of constant block-sum designs using Galois field. In this direction, the construction of constant block-sum Youden-m square designs and the constant block-sum Partially Balanced Incomplete Block (PBIB) designs has been discussed. In addition to this, a generalized m-associate class association scheme, on which the PBIB designs constructed in this paper are based, is also discussed.

Keywords:

• Association scheme
• Constant block-sum designs
• Galois field
• PBIB designs
• RCBD
• Youden-m square designs

MATHEMATICAL SUBJECT CLASSIFICATION:

• 05E30
• 62K10
• 05B05
• 62K99

Acknowledgments

The authors are highly thankful to the reviewer for suggesting valuable additions and corrections which make the paper more presentable.