<![CDATA[Experimental designs based on Hyper Blocks Graeco-Latin Sudoku Squares have predominantly been analyzed within single environments using fixed-effects models, limiting their applicability to experiments conducted across multiple locations or seasons. This study introduced a combined analytical framework for several experiments conducted under different environments with identical treatments. To address the limitations of conventional approaches, environmental effects and treatment-by-environment interactions were incorporated into the Hyper Blocks Graeco-Latin Sudoku Square Design (HBGLSSD) framework using mixed-effects models. Hypothetical and simulated datasets were generated and analyzed using R software. The efficiency of the multi-environment HBGLSSD was evaluated against that of the conventional HBGLSSD based on mean square error, p-values, and the statistical power of the F test. The results indicate that incorporating environmental effects and treatment-by-environment interactions improves analytical precision and efficiency, as evidenced by lower error mean squares and greater test power. The proposed framework therefore provides a more robust basis for analyzing HBGLSSD experiments conducted under heterogeneous environmental conditions. This study extends Sudoku-based experimental design methodology by accommodating cross-environment variation and offers a practical analytical approach for multi-location or multi-season experiments involving common treatments.]]>
