How to construct resolution III fractional factorial designs

Resolution IV designs are easily constructed from saturated designs of resolution III. For example, starting from our first 2jh fractional, we can 

Estimates of main effect 5 and all binary interaction effects involving this factor 

With this design we will have to perform twice as many runs, but the additional work is compensated by a gain in resolution. Since the new design is defined by the relations I = 1248 = 1358 = 2368 = 1237, its resolution becomes 4. 

Exercise 4.17. Use the generating relations given in Table 4.15 and find the three- 

With resolution IV designs, we can completely separate all the main effects from the two-factor interactions, as shown in Table 4.16. The contrasts corresponding to the actual columns of the design estimate the main effects of the eight variables, while the contrasts defined by products of two columns estimate combinations of two-factor interactions.  

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