A graphical construction of the D-optimal saturated, 3×s2 main effect, factorial design

This paper considers the incidence (bipartite) graph G, which is associated with a saturated main effect, 3×s2 factorial design. Some certain classes of paths are defined and it is shown that their various combinations determine the upper bound of the value of the determinant of the adjacency matrix. Therefore, a specific type of planar graphs is constructed and the main goal of this result is the production of D-optimal plans for each s⩾3.