Efficiency of Sum Constructed Automorphic Symmetric Balanced Incomplete Block Designs

Several construction methods have been introduced to build the elements of balanced incomplete block designs (BIBDs) for specific parameters, with different techniques suggested for testing their existence. There is still no general technique to determine the existence of the designs that have been realized. In this study the efficiencies of some given automorphic symmetric balanced incomplete block designs (AUSBIBD) formed by sum construction method have been presented in details alongside existence and non-existence of such designs. The process involved the application of sum construction method to give new designs of parameters D (v, b, λ1+λ2) and an application of Bruck Ryser Chwola theorem extensively. A test design constructed using the described method was found to be existing with an efficiency of 76.38%. Sum constructed designs are more applicable in agricultural fields as witness in case of KEFRI-Kenya.