Sum Construction of Automorphic Symmetric Balanced Incomplete Block Designs

C.W. Otulo¹ , Z.M. Muga² , N.B. Okelo³ , J.O. Nyakinda⁴

Section:Research Paper, Product Type: Journal-Paper
Vol.7 , Issue.4 , pp.10-13, Aug-2020

Online published on Aug 31, 2020

Copyright © C.W. Otulo, Z.M. Muga, N.B. Okelo, J.O. Nyakinda . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
In this study Sum construction method of automorphic symmetric balanced incomplete block designs has been presented in details. Efficiency of a test design used in the Sum construction of automorphic symmetric balanced incomplete block designs has been determined alongside its existence. The process involved the application of sum construction to give new designs of parameters D (v, b, λ1+λ2) and an application of Bruck Ryser Chwola theorem extensively. A test design used in the sum construction method has been found to be existing with an efficiency of 77.78%. The sum constructed automorphic symmetric balanced incomplete block designs provide more information per block than the parent designs

Key-Words / Index Term :
Symmetric Balanced Incomplete Block Design (SBIBD), Automorphism and Automorphic Symmetric Balanced Incomplete Block Design(AUSBIBD)

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