Several mathematical studies ham been carried out to help solve spe• rilir- probk-ius 1wrht.iuiug t11 t•lt<• «onsrrncrtou mu! nnnlvsis of Dafaw•,•d Incomplete Block designs in terms of application. Most of these studies arc centered at variation in the number of groups. block sizes and the pair of distinct treatments within tilt' sumo group ,.\, Although most of the construction methods have been introduced to build the clements of designs for specific parameters. with different techuiqucs suggested for testing their existence, no general tcclmiquc for determining the oxis• tr-nee of these• designs has been realized. There is no existing algorithm on the sum construction method of Autoiuorphic Symmetric Balanced Incomplorr- Block Designs. The main objective of this study is to per• form sum construction of Automorphic Symmetric Balanced Incomplete Block Designs alongside developing an algorithm, establishing tho cxis• I cnce and dctcnutning tho clliciency of s11111 constructed Antoruorplur Symmetric Balanced Incomplete Block Designs. A method of Classical Analysis of variaucc has been employed in the detcnuiuatiou of rolar.ive cllicicucv of the sum cousuuctcd Designs nud a discussion on practical application of such designs is presented based on the generated analysis of variance tables. The findiugs reveal that a sum constructed rlesigu has ,, higher number of significant variables houce more cffirieut with 11 relative dfir:iPncy of l.21G whr-n compare.I with t hr- parent ,Jc.si.e;n. This suulv enriches the area of cxprriuiontal design by providing techniques used in selection of blocks and contributes to the academic world by introducing an algorithm for sum construction of Autoiuorphic Symmetric Balanced Incomplete Block Designs.