Fold-over design to resolve main effects from confoundings with two-variable interactions

Fold-over design to resolve main effects from confoundings with two-variable interactions 

This section presents a technique, by which a complemetary fraction can be found which can resolve all main effects from confoundings with two-variable interaction effects. 

Assume that a 2 fractional factorial screening experiment has been run with seven variables, and where the extra variables have been defined as 4 = 12, 

By making all possible multiplications of these, the following rather large complete set of generators is obtained 

Each estimate from this design will be an alias of 16 confounded effects. If we consider only main effects and two-variable interaction effects and ignore all higher interactions, the following estimates can be obtained  

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