A Complete Catalog of Geometrically Non-Isomorphic 18-run Orthogonal Arrays

Factorial designs have wide applications in industrial and scientific studies. Traditionally, they are classified based their combinatoric properties. Two designs are considered to be isomorphic if one can be obtained by permuting of the factors and level permutation within factors. Such isomorphism treats levels of each factor nominal without natural ordering and is often referred as combinatoric isomorphism. (Chang and Ye, 2004). However, many researchers has realized that when factors are quantitative, level permutations of a factorial design often result changes in design properties such as estimation efficiencies, and the combinatoric isomorphism