Journal of Systems Science and Complexity

, Volume 20, Issue 3, pp 429–436 | Cite as

Construction of a New Class of Orthogonal Arrays

  • Shanqi PangEmail author


By using the generalized Hadamard product, difference matrix and projection matrices, we present a class of orthogonal projection matrices and related orthogonal arrays of strength two. A new class of orthogonal arrays are constructed.


Difference matrix mixed-level orthogonal array permutation projection matrix 


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  1. 1.
    A. S. Hedayat, N. J. A. Sloane, and J. Stufken, Orthogonal Arrays: Theory and Applications, Springer, New York, 1999.Google Scholar
  2. 2.
    R. C. Bose and K. A. Bush, Orthogonal arrays of strength two and three, Ann. Math. Stat., 1952, 23(4): 508–524.Google Scholar
  3. 3.
    C. F. J. Wu, R. Zhang, and R. Wang, Construction of asymmetrical orthogonal array of the type OA\((s^{k},s^{m}(s_{1}^{r})^{n_1}\cdots (s_{t}^{r})^{n_t})\) , Statist. Sinica, 1992, 2(1): 203–219.Google Scholar
  4. 4.
    J. C. Wang, Mixed difference matrices and the construction of orthogonal arrays, Statist. Probab. Lett., 1996, 28: 121–126.CrossRefGoogle Scholar
  5. 5.
    S. Q. Pang, Y. S. Zhang, and S. Y. Liu, Further results on the orthogonal arrays obtained by generalized Hadamard product, Statist. Probab. Lett., 2004, 69(1): 431–437.CrossRefGoogle Scholar
  6. 6.
    C. Y. Suen and W. F. Kuhfeld, On the construction of mixed orthogonal arrays of strength two, J. Statist. Plann. Inference, 2005, 133(2): 555–560.CrossRefGoogle Scholar
  7. 7.
    Y. S. Zhang, S. Q. Pang, and Y. P. Wang, Orthogonal arrays obtained by the generalized Hadamard product, Discrete Mathematics, 2001, 238: 151–170.CrossRefGoogle Scholar
  8. 8.
    Y. S. Zhang, Y. Q. Lu, and S. Q. Pang, Orthogonal arrays obtained by orthogonal decomposition of projection matrices, Statist. Sinica, 1999, 9(2): 595–604.Google Scholar
  9. 9.
    S. Q. Pang, S. Y. Liu, and Y. S. Zhang, A note on orthogonal arrays obtained by orthogonal decomposition of projection matrices, Statist. Probab. Lett., 2003, 63(4): 411–416.CrossRefGoogle Scholar
  10. 10.
    J. C. Wang and C. F. J. Wu, An approach to the construction of asymmetrical orthogonal arrays, J. Amer. Statist. Assoc., 1991, 86: 450–456.CrossRefGoogle Scholar
  11. 11.
    W. F. Kuhfeld and C. Y. Suen, Some new orthogonal arrays OA\( (4r,r^{1}2^p,2)\) , Statist. Probab. Lett., 2005, 75(3): 169–178.CrossRefGoogle Scholar

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© Springer Science + Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of MathematicsHenan Normal UniversityXinxiangChina

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