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An isomorphism check for two-level fractional factorial designs. (English) Zbl 1130.62078
Summary: Two fractional factorial designs are isomorphic if one can be obtained from the other by reordering the treatment combinations, relabelling the factor levels and relabelling the factors. By defining a word-pattern matrix, we are able to create a new isomorphism check which is much faster than existing checks for certain situations. We combine this with a new, extremely fast, sufficient condition for non-isomorphism to avoid checking certain cases. We then create a faster search algorithm by combining the D. Bingham and R. R. Sitter [Minimum aberration fractional factorial split-plot designs. Technometrics 41, 62–70 (1999)] search algorithm and the isomorphism check algorithm of J. B. Clark and A. M. Dean [Equivalence of fractional factorial designs. Stat. Sin. 11, No. 2, 537–547 (2001; Zbl 0980.62058)] with our proposed isomorphism check. The algorithm is used to extend the known set of existing non-isomorphic 128-run two-level regular designs with resolution $$\geqslant 4$$ to situations with 12, 13, 14, 15 and 16 factors, 256- and 512-run designs with resolution $$\geqslant 5$$ and $$\leqslant 17$$ factors and 1024-run even designs with resolution $$\geqslant 6$$ and $$\leqslant 18$$ factors.

##### MSC:
 62K15 Factorial statistical designs 65C60 Computational problems in statistics (MSC2010) 62Q05 Statistical tables
##### Keywords:
design equivalence; eigenvalue; eigenvector; Hamming distance
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##### References:
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