Construction of magic squares and partially balanced incomplete block designs

Magic squares are known to mankind since ages. With their eye catching properties, they have attracted and inspired researchers to further explore and work with them. The present paper is written with an aim to explore the usefulness of magic squares in the construction of partially balanced incomplete block (PBIB) designs. In this regard, we have proposed a new method for the construction of magic squares and studied their properties. We have also established a link between these properties and some existing association schemes. We have then introduced four new association schemes using these properties which have been later used for the construction of PBIB designs.