Sum Construction of Automorphic Symmetric Balanced Incomplete Block Designs

Abstract

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.