, where for each level combination of the whole-plot factors only two runs as mirror images are used,
are very run-efficient. These designs are useful in many practical situations. Typical examples include treatments to be
applied to subjects with two eyes, two ears, or two feet, or animal litters of two being easier to obtain than of four or more.
In these situations the proposed designs will yield useful and effective alternatives. Moreover these designs split s and ws
effects and w, ww and ss effects into two orthogonal sub-spaces, which simplify the identification of active factors and also
the estimation of active effects. This is discussed further in