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The doehlert-klee problem: Part I, statistical background

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Part of the Lecture Notes in Mathematics book series (LNM,volume 686)

Keywords

  • Orthogonal Basis
  • Balance Incomplete Block Design
  • Distance Pattern
  • Voronoi Polyhedron
  • Pairwise Balance Design

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References

  1. Conner, W.S., Jr., "On the Structure of Balanced Incomplete Block Designs", Ann. Math. Stat. 23 (1952), 52–71.

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  2. Collens, R.J., "Constructing BIBD's with a Computer", Ars Combinatoria 2 (1976), 285–303.

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  3. Doehlert, D.H., "Uniform Shell Designs", J. Royal Stat. Soc. C, 19 (1970), 231–239.

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  4. Doehlert, D.H. and Klee, V.L., "Experimental Designs Through Level Reduction of the d-dimensional Cuboctahedron", Discrete Math. 2 (1972), 309–334.

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  5. McCarthy, D. and Vanstone, S.A., "On the Structure of Regular Pairwise Balanced Designs", submitted to Discrete Math.

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  6. McCarthy, D., Stanton, R.G. and Vanstone, S.A., "On an Extremal Class of (r, λ) Designs Related to a Problem of Doehlert and Klee", Ars Combinatoria 2 (1976).

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  7. Plackett, R.L. and Burman, J.P., "The Design of Optimum Multifactor Experiments", Biometrika 33 (1946), 305–325.

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  8. Stanton, R.G., "Results on (r, λ) Designs", Cong. Num. 18 (Proc. 6th Manitoba Conf. on Numerical Maths.), Winnipeg (1976), 411–412.

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  9. Stanton, R.G., "Some Results on Block Lengths in (r, λ) Designs", Ars Combinatoria 2 (1976), 213–219.

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  10. Stanton, R.G. and Vanstone, S.A., "Further Results on a Problem of Doehlert and Klee", to appear, Utilitas Math.

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  11. Stanton, R.G. and Vanstone, S.A., "On a Problem of Doehlert and Klee", Cong. Num. 19 (Proc. Eighth S.E. Conf. on Combinatorics, Graph Theory, and Computing)", Baton Rouge (1977) to appear.

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  12. Stanton, R.G. and Vanstone, S.A., "Some Lower Bounds on the Size of Doehlert-Klee Designs", to appear, Ars Combinatoria.

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  13. Stanton, R.G. and Vanstone, S.A., "Some Theorems on DK Designs", preprint.

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  14. Scheffé, H., "The Simplex-centroid Design for Experiments with Mixtures", J. Royal Stat. Soc. B, 25(1963), 235–263.

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© 1978 Springer-Verlag

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Stanton, R.G. (1978). The doehlert-klee problem: Part I, statistical background. In: Holton, D.A., Seberry, J. (eds) Combinatorial Mathematics. Lecture Notes in Mathematics, vol 686. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062520

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  • DOI: https://doi.org/10.1007/BFb0062520

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08953-7

  • Online ISBN: 978-3-540-35702-5

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