Construction of uniform designs via super-simple resolvable t-designs

Utilitas Mathematica

Volumn 66, Issue , 2004, Pages 15-32

  Fang, Kai Tai ^a   Ge, Gen Nian ^b   Liu, Min Qian ^c   Qin, Hong ^a,d  

^a HONG KONG BAPTIST UNIVERSITY   (Hong Kong)

^b ZHEJIANG UNIVERSITY   (China)

^c NANKAI UNIVERSITY   (China)

^d CENTRAL CHINA NORMAL UNIVERSITY   (China)

Author keywords

MGA; Nearly orthogonal design; Resolvable t design; Super simple; U type design; Uniform design

Indexed keywords

EID: 13244279537     PISSN: 03153681     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (29)

1. R. J. R. Abel, L. Bluskov and M. Greig, Balanced incomplete block designs with a block size 8, J. Combin. Designs 9 (2001), 233-268.
2. R. J. R. Abel, G. N. Ge, M. Greig and L. Zhu, Resolvable balanced incomplete block designs with a block size of 5, J. Statist. Plann. Inference 95 (2001), 49-65.
3. T. Beth, D. Jungnickel and H. Lenz, Design Theory, Cambridge University Press, 1999.
4. C. J. Colbourn and J. H. Dinitz, CRC handbook of combinatorial designs, CRC Press Inc, Boca Raton, 1996. (New results are reported at http://www.emba.uvm.edu/~dinitz/newresults.html)
5. K.T. Fang, The uniform design: application of number-theoretic methods in experimental design, Acta Math. Appl. Sinica 3 (1980), 363-372.
6. K.T. Fang, Some applications of Quasi-Monte Carlo methods in statistics, in: Monte Carlo and Quasi-Monte Carlo Methods 2000, eds. by K. T. Fang, F. J. Hickernell, and H. Niederreiter, Springer-Verlag, Berlin, 2002, 10-26.
7. K. T. Fang, G. N. Ge and M. Q. Liu, Construction of optimal supersaturated designs by the packing method, Technical Report MATH-308, Hong Kong Baptist University, 2001.
8. K. T. Fang, G. N. Ge, M. Q. Liu and H. Qin, Construction of minimum generalized aberration designs, Metrika, 2002, to appear.
9. K. T. Fang and D. K. J. Lin, Uniform experimental designs and their applications in industry, in: Handbook of Statistcs, Vol 23, ed. Rao, C. R. and Khattree, R., 2002.
10. K. T. Fang, D. K. J. Lin and M. Q. Liu, Optimal mixed-level supersaturated design and computer experiment, Technical Report MATH-286, Hong Kong Baptist University, 2000.
11. K. T. Fang, D. K. J. Lin, P. Winker and Y. Zhang, Uniform design: theory and applications, Technometrics 42 (2000), 237-248.
12. 2 -discrepancy of random sampling and Latin hypercube design, and construction of uniform design, Math. Comp. 71 (2002), 275-296.
13. K. T. Fang, C. X. Shiu and J. X. Pan, Uniform designs based on Latin squares, Statist. Sinica 9 (1999), 905-912.
14. K. T. Fang and Y. Wang, Number-Theoretic Methods in Statistics, Chapman & Hall, London, 1994.
15. n-m designs, Technometrics 26 (1984), 225-232.
16. k-p designs, Technometrics 22 (1980), 601-608.
17. G. N. Ge and C. W. H. Lam, Super-simple resolvable balanced incomplete block designs with block size 4 and index 3, Submitted for publication, 2002.
18. A. Hartman, The existence of resolvable Steiner quadruple systems, J. Combin. Theory, Ser. A 44 (1987), 182-206.
19. F. J. Hickernell, A generalized discrepancy and quadrature error bound, Math. Comp. 67 (1998), 299-322.
20. F. J. Hickernell and M. Q. Liu, Uniform designs limit aliasing, Technical Report MATH-275, Hong Kong Baptist University, 2000.
21. M. Q. Liu, Using discrepancy to evaluate fractional factorial designs, in: Monte Carlo and Quasi-Monte Carlo Methods 2000, eds. by K. T. Fang, F. J. Hickernell, and H. Niederreiter, Springer-Verlag, Berlin, 2002, 357-368.
22. 2)-optimality and minimum discrepancy in 2-level supersaturated designs, Statist. Sinica 12 (2002), 931-939.
23. C. X. Ma and K. T. Fang, A note on generalized aberration factorial designs, Metrika 53 (2001), 85-93.
24. C. X. Ma, K. T. Fang and E. Liski, A new approach in constructing orthogonal and nearly orthogonal arrays, Metrika 50(2000) , 255-268.
25. R. Rees and D. R. Stinson, Frames with block size four, Canad. J. Math. 44 (1992), 1030-1049.
26. H. Shen, Resolvable twofold tripe systems without repeated blocks, Kexue Tongbao (Science Bulletin) 33 (1988), 1855-1857.
27. J. C. Wang and C. F. J. Wu, Nearly othogonal arrays with mixed levels and small runs, Technometrics 34 (1992), 409-422.
28. P. Winker and K. T. Fang, Application of Threshold accepting to the evaluation of the discrepancy of a set of points, SIAM Numer. Analysis 34 (1997), 2038-2042.
29. P. Winker and K. T. Fang, Optimal U-type design, in: Monte Carlo and QuasiMonte Carlo Methods 1996, eds. by H. Niederreiter, P. Zinterhof and P. Hellekalek, Springer, 1998, 436-448.