Construction of Generalized Incomplete Trojan-Type Designs

M. NAWAZ, M. M. IQBAL, I. IQBAL

Abstract


For crop research, near-Latin square and Latin square are important and very useful row-and-column designs, especially in greenhouse experiments, however, practical range of these designs are very scarce. Semi-Latin Square Designs (SLSD) do cover this range but have limited usability. Trojan Square Designs is classified into Optimal Semi-Latin Squares (OSLS) that generalizes the class of Latin Square Designs. By a discussion of Incomplete Trojan Square Designs (ITSD) attained by removing a single key row or column from a complete Trojan Square Design, body of already existing designs is drawn out to a greater extent. In this article, we introduce some constructions of Generalized Incomplete Trojan-Type Designs (GITTD) for𝑘 = 2, 3, 4, 5, 6. Some of the designs are pair- wise balanced or variance balanced and the remaining are regular graphs.


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