Non-orthogonal Blocked Two-level Factorial Designs

When orthogonal blocking of orthogonal designs is not possible, we will have to allow either non-orthogonality between treatment factors or non-orthogonality between treatments and blocks. An example of this situation is running an experiment with a 12-run design of 5 factors in three blocks. Two approaches are studied, and their performances in estimation efficiency of treatment main effects are compared. Some best designs of 12 runs in three blocks and of 20 runs in five blocks are found and tabulated.