New recommended designs for screening either qualitative or quantitative factors

By the affine resolvable design theory, there are 68 non-isomorphic classes of symmetric orthogonal designs involving 13 factors with 3 levels and 27 runs. This paper gives a comprehensive study of all these 68 non-isomorphic classes from the viewpoint of the uniformity criteria, generalized word-length pattern and Hamming distance pattern, which provides some interesting projection and level permutation behaviors of these classes. Selecting best projected level permuted subdesigns with 3≤ k≤ 13 factors from all these 68 non-isomorphic classes is discussed via these three criteria with catalogues of best values. New recommended uniform minimum aberration and minimum Hamming distance designs are given for investigating either qualitative or quantitative 4≤ k≤ 13 factors, which perform better than the existing recommended designs in literature and the existing uniform designs. A new efficient technique for detecting non-isomorphic designs is given via these three criteria. By using this new approach, in all projections into 1≤ k≤ 13 factors we classify each class from these 68 classes to non-isomorphic subclasses and give the number of isomorphic designs in each subclass. Close relationships among these three criteria and lower bounds of the average uniformity criteria are given as benchmarks for selecting best designs.