Interchanges and statistical designs

Let D be a statistical design consisting of v varieties on b blocks. We say it is binary if a variety occurs at most once on every block. For varieties p and q on blocks x and y respectively, we can obtain design D' from D by interchanging p and q (so p is on y and q is on x). We say that the exchange is binary if either x y, or p q, or: q not on x and p not on y. If D is binary then D' is also binary. We examine the equivalence classes for binary designs under binary interchanges. This work is relevant in the construction of certain classes of optimal or nearoptimal designs.