In this paper, we consider experimental situations where a main effects plan is to be used to study m two-level factors using n runs which are partitioned into b blocks of equal size k = n/b. It is shown that when n ≡ 2 (mod 8) and k > 2, the best possible design under the D-optimality criterion does not necessarily have all factors orthogonal to blocks. In such situations, an alternative class of designs is suggested for usage which are better under the D-optimality criterion than the best available design having all main effects orthogonal to blocks.
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机译：在本文中，我们考虑了实验情况，在该情况下，将使用n个运行划分为b个大小相等的k = n / b块的主运行计划，以研究m个二级因素。结果表明，当n≡2（模数8）且k> 2时，在D优化准则下的最佳设计不一定具有与块正交的所有因子。在这种情况下，建议使用替代设计类别，在D优化准则下，该设计要比具有所有正交于块的主要效果的最佳可用设计更好。
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