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A replacement procedure to construct orthogonal arrays of strength three was proposed by Suen et al. [7]. This method was later extended by Suen and Dey [8]. In this paper, we further explore the replacement procedure to obtain some new families of orthogonal arrays of strength three.
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Orthogonal array and a large set of orthogonal arrays are important research objects in combinatorial design theory, and they are widely applied to statistics, computer science, coding theory, and cryptography. In this paper, some new series of large sets of orthogonal arrays are given by direct construction, juxtaposition construction, Hadamard construction, finite field construction, and difference matrix construction. Subsequently, many new infinite classes of orthogonal arrays are obtained by using these large sets of orthogonal arrays and Kronecker product.
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