Catalogue of small runs nonregular designs from Hadamard matrices with generalized minimum aberration

Fries and Hunter (1980) proposed the Minimum Aberration Criterion (Mb) for selecting regular designs. The regular designs with MA are most commonly used because they are considered as the best designs. However, as pointed out by Chen, Sun and Wu (1993), there are situations that other designs may better meet the design need. Therefore, they catalogued some two-level and three-level fractional factorial regular designs with small (16,27,32,64) runs. For nonregular designs, such as the ones taken from Hadamard matrices, the MA criterion is not applicable. Deng and Tang (1999) introduced Generalized Minimum Aberration Criterion (GMA) as a natural extension to the MA criterion. Similar to the case in the regular designs, other designs may better meet practical need. In this paper, we use the GMA criterion to give a catalogue of nonregular designs with small (16, 20, 24) runs.