Abstract: Among all 2n-k regular fractional factorial designs, minimum aberration designs are often preferred. When 2n-k (the run-size) is no more than 64, most (possibly all) minimum aberration designs have been found. When 2n-k, the search for minimum aberration designs becomes very hard. The results in Chen and Wu (1991) and Chen (1992) include all 128-run minimum aberration designs with k<=5. When n is close to 2n-k , Tang and Wu (1996) also obtain some minimum aberration designs. In this paper, we search for 128-run minimum aberration designs with k=6 and k=7. By combining theoretical understanding with intelligent computer search, both cases are solved.
Key words and phrases: Defining contrast subgroup, fractional factorial design, wordlength pattern.