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An approach of constructing mixed-level orthogonal arrays of strength ⩾ 3

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Abstract

Orthogonal arrays (OAs), mixed level or fixed level (asymmetric or symmetric), are useful in the design of various experiments. They are also a fundamental tool in the construction of various combinatorial configurations. In this paper, we establish a general “expansive replacement method” for constructing mixedlevel OAs of an arbitrary strength. As a consequence, a positive answer to the question about orthogonal arrays posed by Hedayat, Sloane and Stufken is given. Some series of mixed level OAs of strength ⩾ 3 are produced.

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References

  1. Brouwer A E, Cohen A M, Nguyen M V M. Orthogonal arrays of strength 3 and small run sizes. J Statist Plann Infer, 2006, 136: 3268–3280

    Article  MathSciNet  MATH  Google Scholar 

  2. Bush K A. Orthogonal arrays of index unity. Ann Math Stat, 1952, 23: 426–434

    Article  MathSciNet  MATH  Google Scholar 

  3. Bush K A. A generalization of the theorem due to MacNeish. Ann Math Stat, 1952, 23: 293–295

    Article  MathSciNet  MATH  Google Scholar 

  4. Cohen M B, Gibbons P B, Mugridge W B, et al. Variable strength interaction testing of components. In: Proceedings of the 27th Annual International Computer Software and Applications Conference. Dallas, TX: IEEE Computer Society Washington, 2003, 413–418

    Google Scholar 

  5. Colbourn C J, Dinitz J. H. The CRC Handbook of Combinatorial Designs. Boca Raton, FL: CRC Press, 2007

    MATH  Google Scholar 

  6. Dey A, Mukerjee R. Fractional Factorial Plans. New York: John Wiley & Sons, Inc, 1999

    Book  MATH  Google Scholar 

  7. Hedayat A S, Sloane N J A, Stufken J. Orthogonal Arrays. New York: Springer, 1999

    Book  MATH  Google Scholar 

  8. Ji L, Yin J. Constructions of new orthogonal arrays and covering arrays of strength three. J Combin Theory A, 2010, 117: 236–247

    Article  MathSciNet  MATH  Google Scholar 

  9. Nguyen M V M. Some new constructions of strength 3 mixed orthogonal arrays. J Statist Plann Infer, 2008, 138: 220–233

    Article  MATH  Google Scholar 

  10. Yan J, Zhang J. Combinatorial Testing: Principles and Methods (in Chinese). J Softw, 2009, 20: 1393–1405

    Article  Google Scholar 

  11. Wang Z Y, Xu B W, Nie C H. Survey of combinatorial test generation (in Chinese). J Frontiers Comput Sci Technology, 2008, 2: 571–588

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Soochow University, Suzhou, 215006, China

    Ling Jiang & JianXing Yin

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  1. Ling Jiang
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  2. JianXing Yin
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Correspondence to JianXing Yin.

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Jiang, L., Yin, J. An approach of constructing mixed-level orthogonal arrays of strength ⩾ 3. Sci. China Math. 56, 1109–1115 (2013). https://doi.org/10.1007/s11425-013-4616-y

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  • DOI: https://doi.org/10.1007/s11425-013-4616-y

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