For the majority of run sizes N where N <= 20, the literature reports the best D- and A-optimal designs for the main-effects model which sequentially minimizes the aliasing between main effects and interaction effects and among interaction effects. The only series of run sizes for which all the minimally aliased D- and A-optimal main-effects designs remain unknown are those with run sizes three more than a multiple of four. To address this, in our paper, we propose an algorithm to generate all non-isomorphic D- and A-optimal main-effects designs for run sizes three more than a multiple of four. We enumerate all such designs for run sizes up to 19, report the numbers of designs we obtained, and identify those that minimize the aliasing between main effects and interaction effects and among interaction effects.

翻译：对于大多数试验量N（N ≤ 20），现有文献已报道了针对主效应模型的最佳D-与A-最优设计，这些设计依次最小化了主效应与交互效应之间以及交互效应之间的别名效应。在所有试验量系列中，唯一尚未确定所有最小别名D-与A-最优主效应设计的系列是试验量比4的倍数多3的情况。为此，本文提出一种算法，用于生成所有非同构的D-与A-最优主效应设计，适用于试验量比4的倍数多3的情形。我们枚举了试验量不超过19的所有此类设计，报告了所得设计的数量，并从中识别出能够最小化主效应与交互效应之间以及交互效应之间别名效应的设计。