Strong Orthogonal Arrays of Near Strength Two Plus

In computer experiments, space-filling designs with superior low-dimensional projections are highly desirable. Strong orthogonal arrays (SOAs) of strength (Formula presented.) are particularly practical among various space-filling designs, as they offer excellent two-dimensional stratification properties. However, an SOA of strength (Formula presented.) typically has significantly fewer columns than an orthogonal array (OA) of strength 2. To make a balance between two-dimensional projection uniformity and the number of factors, this paper introduces a new class of arrays termed as strong orthogonal arrays of near strength (Formula presented.). These arrays can accommodate more factors than SOAs of strength (Formula presented.) while retaining attractive low-dimensional projection properties, thus providing experimenters with more options. We investigate the theoretical properties of this new class of arrays and propose two efficient algorithmic construction methods. The resulting designs are flexible in size and integrates the advantages of SOAs of strength (Formula presented.) and OAs of strength 2. Numerical comparisons with existing designs and a computer experiment simulation study demonstrate the superiority of the new designs.