Construction and analysis of Incomplete Balanced and Partially Balanced Sudoku Square Designs

Sudoku Square Designs, represent a Statistical extension of Latin Square design (LSD), distinguished by their ability to incorporate an additional effect, namely the subzone effect, without increasing the number of experimental plots. This feature introduces an added layer of complexity compared to traditional LSD or row column designs, A grid square of order n is divided into n subzones of dimensions a × b (where a × b = n and a = b or a ≠ b ), ensuring each of the n elements appears precisely once in every row, column, and subzone. Furthermore, the statisticians are increasingly draw to Sudoku Square Design due to their broad applications. This article focusing on the construction and analysis of Balanced and Partially Balanced Sudoku Square Designs with fewer treatments. It presents methods for constructing symmetrical and asymmetrical Sudoku Square Designs, accompanied by illustrative examples for clarity. Information matrices for analyzing these designs are developed, and comprehensive lists of constructed designs are provided. Analysis of one field trail level trail on Balanced Sudoku square designs and one field trail of Partially Balanced Sudoku square design had been incorporated for better understanding of the analysis of designs.