A Note on the Lower Bounds on Maximum Number of Clear Two-Factor Interactions for (2^m−p_III) and (2^m−p_IV) Designs

Abstract

Clear effects criterion is one of the most important rules for selecting 2 ^m−p designs, and it is valuable to know the maximum number of clear two-factor interactions in 2 ^m−p designs. This article provides lower bounds on the maximum number of clear two-factor interactions for and designs by constructing specific designs, respectively. The lower bounds improve the ones given in Tang et al. (2002) and the construction methods perform quite well.

Keywords:

• Clear effects
• Resolution
• Two-factor interaction
• Wordlength pattern

Mathematics Subject Classification:

• Primary 62K15
• Secondary 62K05

Acknowledgments

This work was partially supported by the National Natural Science Foundation of China grant 10301015, the Science and Technology Innovation Fund of Nankai University, and the Visiting Scholar Program at Chern Institute of Mathematics.

Notes

AC(m): all the additional columns of the design in this table.

AC(m, k): all the additional columns of the design in this table.