Summary of Plackett-Burman Designs
main topic 

These are the designs given in [7], up through n = 48, where n is the number of runs. In all cases except n = 28, the design can be specified by giving just the first column of the design matrix. In the table below, we give this first column (written as a row to save space). This column is permuted cyclically to get an (n - 1) x (n - 1) matrix. Then a last row of all minus signs is added. For n = 28, we start with the first 9 rows. These are then divided into 3 blocks of 9 columns each. Then the 3 blocks are permuted (rowwise) cyclically and a last column of all minus signs is added to get the full design.

Each design can have up to k = (n - 1) factors. If you specify a k that is less than (n - 1), just the first k columns are used.

12 Runs

 + + - + + + - - - + -

20 Runs

 + + - - + + + + - + - + - - - - + + -

24 Runs

 + + + + + - + - + + - - + + - - + - + - - - -

28 Runs

 + - + + + + - - - - + - - - + - - + + + - + - + + - +

 + + - + + + - - - - - + + - - + - - - + + + + - + + -

 - + + + + + - - - + - - - + - - + - + - + - + + - + +

 - - - + - + + + + - - + - + - - - + + - + + + - + - +

 - - - + + - + + + + - - - - + + - - + + - - + + + + -

 - - - - + + + + + - + - + - - - + - - + + + - + - + +

 + + + - - - + - + - - + - - + - + - + - + + - + + + -

 + + + - - - + + - + - - + - - - - + + + - + + - - + +

 + + + - - - - + + - + - - + - + - - - + + - + + + - +

32 Runs

 - - - - + - + - + + + - + + - - - + + + + + - - + + - + - - +

36 Runs

 - + - + + + - - - + + + + + - + + + - - + - - - - + - + - + + - - + -

40 Runs (note, derived by duplicating the 20 run design)

 + + - - + + + + - + - + - - - - + + - + + - - + + + + - + - + - - - - + + -

44 Runs

 + + - - + - + - - + + + - + + + + + - - - + - + + + - - - - - + - - - + +- + - + + -

48 Runs

 + + + + + - + + + + - - + - + - + + + - - + - - + + - + + - - - + - + - + + - - - - + - - - -