A Nested Balanced Incomplete Block Design (NBIBD) is a design with two systems of blocks, each block from the first system containing m-blocks from the second. Consequently, by ignoring either system of blocks leaves a Balanced Incomplete Block Design (BIBD) whose blocks are those of the other system. Designs k = s2, where s is a prime or prime power. Otherwise the imposed relationship between the parameters of the designs would not be satisfied. In particular, double cyclic design for v = 7 and two distinct double cyclic designs for v = 13 were constructed and presented in Table 1.