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This is a Quantitative Study study.

October 16, 2025

Relative Efficiency of Sum Constructed Automorphic Symmetric Balanced Incomplete Block Designs

COC.W OtuloJaramogi Oginga Odinga University of Science and Technology ZMZ.M MugaJaramogi Oginga Odinga University of Science and Technology BOBenard OkeloJaramogi Oginga Odinga University of Science and Technology

Key Points

The study establishes the relative efficiency of balanced incomplete block designs, reported as 1.216.
Computed relative efficiency is compared between Sum constructed automorphic symmetric designs and parent designs.
Classical analysis of variance was utilized to evaluate the efficiencies in the applied dataset.
Results indicate that improved efficiencies may be achieved by utilizing automorphic symmetric designs.

Abstract

Several construction methods have been introduced to build the elements of BIBDs’ for specific parameters, with different techniques suggested for testing their existence, still no general technique to determine the efficiencies of these designs has been realized. In this study the efficiencies and relative efficiencies of Sum constructed automorphic symmetric balanced incomplete block designs with respect to parent designs has been presented. The process involved the classical analysis of variance applied to a data set. Computed relative efficiency of the design λ3 with respect to parent design λ1 has been found to be 1.216.

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