Minimum Aberration Fractional Factorial Designs With Large N

Abstract

Xu has cataloged 165 minimum aberration (MA) regular fractional factorial (FF) designs with 2-levels and large run sizes N=128 (m=8–64 factors), N=256 (m=9–28, 109–119), N=512 (m=10–25, 238–246), N=1024 (m=11–24, 488–501), N=2048 (m=12–23), and N=4096 (m=13–24). Such an extensive catalog was produced because of an improved algorithm. We extend the catalog by 36 MA, 2-level regular FF designs: N=256 (m=29–36, 100–108), N=512 (m=26–29), N=1024 (m=25–28), N=2048 (m=24–32), and N=4096 (m=25–26). Although such enumeration problems are notoriously difficult with increased N and/or m, we brought the newly solved problems within computational reach by changing the vital isomorphism check component of Xu’s algorithm. Here we present a new, compact graph for solving regular design isomorphism problems and use the nauty program to solve the corresponding graph isomorphism problems. Supplemental appendices are available online.

Keywords:  :

• Bipartite undirected graph
• Graph theory
• Word-length pattern