A construction of non self-orthogonal designs

It is known that a self-orthogonal 2-(21,6,4)(21,6,4) design is unique up to isomorphism. We give a construction of 2-(21,6,4)(21,6,4) designs. As an example, we obtain non self-orthogonal 2-(21,6,4)(21,6,4) designs. Furthermore, we also consider a generalization of the construction.