Consider blocking a 2 × 32 × 4 factorial into six blocks of 12 treatment combinations each.

(a) Naming the factors A, B, C, and D, which factors must be represented by pseudo factors in order to block using the classical method?

(b) What are the two sub-experiments composed of factorials with prime number of levels?

(c) What interactions of factors and pseudo factors would you confound in each sub-experiment in order to allow estimation of the main eects?

What eects and interactions will be unconfounded with blocks and estimable?

(d) Create the design using the mod function as shown in Section 7.8.1.

(e) Can you create a design using the optBlock function in the AlgDesign package that has six blocks of 12 and allows estimation of all two-factor interactions?