Sum Construction of Automorphic Bibds and their Applications in Experimental Designs

In this paper, a construction equivalent to "sum construction", of BIBDs where BIBD is added to a BIBD that is automorphic to it is presented. The result is that we can get new BIBDs by forming the collection of t-(ν,k,λt) BIBD with its automorphic BIBDs. A new recursive technique has been developed for the construction of designs. It has also clearly shown that every t-design is also a BIB (ν,k,λt) design. Therefore, this construction technique also generates BIBDs. Therefore, this note presents an alternative method that is simpler and unified for the construction of BIBDs that are very important in the experimental designs. As it provides designs for different values of k, unlike many methods that provide designs for a single value of k. Moreso, it provides both Steiner and non-Steiner designs.