In chemical and engineering sciences, most factors are quantitative, benefiting from investigation at three distinct levels when studying quadratic or non-linear relationships. Consequently, definitive screening designs (DSDs), a class of 3-level foldover designs introduced by Jones and Nachtsheim (2011), have gained prominence over traditional 2-level designs such as fractional factorial and Plackett-Burman designs. This article extends the framework of conference matrix-based DSDs by introducing a new class of circulant weighing matrix-based screening designs, offering greater design flexibility. Like DSDs and the orthogonal minimally aliased response surface (OMARS) designs recently proposed by N & uacute;& ntilde;ez Ares and Goos (2020), these new designs preserve orthogonality among main effects and between main and second-order effects (i.e., quadratic effects and two-factor interactions), while ensuring the absence of full aliasing among second-order effects. We refer to these designs as OMARS designs to highlight their ability to support both factor screening and response surface exploration in a single step. We present a comprehensive catalog of 149 new OMARS designs with desirable projection capability, accommodating up to 50 factors.
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