Abstract
Mixed-level designs are widely used in various experiments. This paper considers how to construct minimum aberration 4 1 2 n mixed-level designs. Based on finite projective geometry, secondary complementary set is defined as part of the design which plays a crucial role in constructing the optimal designs. Then, algebraic connection between the wordlength pattern of a 4 1 2 n design and that of its secondary complementary set is established. According to the connection, some general rules for identifying type 0 minimum aberration 4 1 2 n mixed-level designs are proposed via their secondary complementary sets. Those rules can help construct minimum aberration 4 1 2 n designs conveniently when the secondary complementary set contains fewer elements than the complementary set. The type 0 minimum aberration 4 1 2 n designs with large n are tabulated via secondary complementary sets.
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