Nesting Plackett-Burman designs

Engineers often perform the runs in an experiment one after another in a sequence of nested designs. It would be desirable, for example, if an experimenter who is planning a Plackett-Burman design for p factors in twenty points could order them so that the first twelve points and the first sixteen points are also Plackett-Burman designs. Unfortunately, if 4 [less-than-or-equals, slant] p [less-than-or-equals, slant] 7, one cannot add four more points to or delete four points from a Plackett Burman design and obtain another Plackett Burman design. It follows that any Plackett Burman design for four factors in twelve runs must contain a pair of duplicate points and any such design for twenty points must have at least five duplicates.