Construction of Balanced n-ary t-designs by Block Sum and Product (BSP) Methodology on 3-designs

In this paper we use 3-designs whose incidence matrix will take only binary values and constructed a series of balanced n-ary t-designs by using a tool Block Sum and Product (BSP) Methodology. The simple 3-(4, 3, 1) and 3-(5, 3, 1) designs are used as a parent 3-designs for the procedure. The parent 3-(4, 3, 1) design gives three new balanced n-ary t-designs and 3-(5, 3, 1) design gives twenty new balanced n-ary t-designs. We given incidence matrices and list out the parameters of newly constructed balanced and partially balanced n-ary t-designs.