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二水平分数因子设计的最优分区组理论AI 解读

In this paper, we define the blocking wordlength pattern of a blocked fractional factorial design by combining the wordlength patterns of treatment-defining words and block-defining words. The concept of minimum aberration can be defined in terms of the blocking wordlength pattern and provides a good measure of the estimation capacity of a blocked fractional factorial design. By blending techniques of coding theory and finite projective geometry, we obtain combinatorial…

q 水平分数因子设计的恒等式及其最小混杂度应用AI 解读

Chen and Hedayat and Tang and Wu studied and characterized minimum aberration $2^{n-m}$ designs in terms of their complemetary designs. Based on a new and more powerful approach, we extend the study to identify minimum aberration $q^{n-m}$ designs through their complementary designs. By using MacWilliams identities and Krawtchouk polynomials in coding theory, we obtain some general and explicit relationships between the wordlength pattern of a $q^{n-m}$ design and that of…