# Blocking and confounding in replicated $2^k$ factorial design

Consider the $2^6$ factorial in 8 blocks of eight each runs with ABCD, ACE and ABEF as the independent effects chosen to be confounded with blocks. Generate a design. Find the other effect of confounding.

I can solve the second part of the question. I found the solution of the first part in a solutions manual (question 7-11) for Montgomery's textbook on the Design and Analysis of Experiments (Wiley, 2001), but I could not understand this table. I want some one to explain this table. If we change the number of blocks, how do we construct the design?

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What have you done (other than finding a solutions manual)? Where did you get stuck? Could you please provide more detail? This looks like a cut-and-paste homework assignment with no context. –  David May 16 '12 at 3:04
I have revised the material from the "Statistical Principle of Research Design and Analysis" by Kuehl. Specially confounding and aliasing structure of design. I am not doing homework just trying to understand the factorial design using the confounding structure by using this kind of problem. When the design is only $2^3$ factorial, the highest order interaction is ABC, in this case we can use the even-odd rule to construct the block, but if the factor size is more than three, there are large number of factor effects combination. In such a case how can we construct the block? –  David May 16 '12 at 9:18