Orthogonal blocking arrangements for 24-run and 28-run two-level designs

Much research has been done concerning 24-run orthogonal two-level designs involving 3–23 factors and 28-run orthogonal two-level designs involving 3–27 factors. The focus of this research was on completely randomized screening designs and led to lists of recommended designs for each number of factors. When using the recommended designs, there is either no aliasing between the main effects and the two-factor interaction effects or only a limited amount. Among all designs with this attractive property, the recommended designs minimize the aliasing among the two-factor interaction effects. It is, however, unclear which 24- and 28-run designs are best when complete randomization is infeasible and the designs have to be arranged in blocks. In this article, we address this issue and present the best arrangements of 24-run designs in 3, 4, and 6 blocks and the best arrangements of 28-run designs in 7 blocks.