Skip to main content
SpringerLink
Log in

D-Optimal First Order Saturated Designs with n ≡ 2mod4 Observations

  • Conference paper
MODA4 — Advances in Model-Oriented Data Analysis

Part of the book series: Contributions to Statistics ((CONTRIB.STAT.))

  • 189 Accesses

Abstract

In experimental situations where n two-level factors are involved and n observations are taken, then the D-optimal first order saturated design is an n × n ±1 matrix with the maximum determinant. In this paper we discuss this problem for n ≡ 2mod4, we summarize all the known results, and we give some new D-optimal designs.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Bridges, G. W., Hall, M. Jr. and Hayden, L. J. (1981). Codes and designs. J. Combin. Theory, Ser. A, 31, 155–174.

    Article  MathSciNet  MATH  Google Scholar 

  • Brouwer, A. E. (1983). An infinite series of symmetric designs. Math. Centrum Amsterdam Report ZW 202/83.

    Google Scholar 

  • Chadjipantelis, T. and Kounias, S. (1985). Supplementary difference sets and D-optimal designs for n m 2mod4. Discrete Math, 57, 211–216.

    Article  MathSciNet  MATH  Google Scholar 

  • Cohn, J. H. E. (1989). On determinants with elements ±1, II. Bull. London Math. Soc., 21, 36–42.

    Article  MathSciNet  MATH  Google Scholar 

  • Cohn, J. H. E. (1992). A D-optimal design of order 102. Discrete Math, 102, 61–65.

    Article  MathSciNet  MATH  Google Scholar 

  • Dokovic, D. Z. (1991). On maximal (1, -1)-matrices of order 2n, n odd. Radovi Maternaticki, 7, 371–378.

    MathSciNet  Google Scholar 

  • Ehlich, H. (1964). Determinantenabschätzung für binäre matrizen. Math. Z., 83, 123–132.

    Article  MathSciNet  MATH  Google Scholar 

  • Kharaghani, H. (1987). A construction of D-optimal designs for n - 2mod4. J. Combin. Theory, Ser A, 46, 156–158.

    MathSciNet  MATH  Google Scholar 

  • Koukouvinos, C., Kounias, S. and Seberry, J. (1991). Supplementary difference sets and optimal designs. Discrete Math, 88, 49–58.

    Article  MathSciNet  MATH  Google Scholar 

  • Seberry, J. and Yamada, M. (1992). Hadamard matrices, sequences and block designs. Contemporary Design Theory: A collection of surveys. Edited by J. Dinitz and D. R. Stinson. J. Wiley and Sons, New York, 431–560.

    Google Scholar 

  • Trung, V. T. (1982). The existence of symmetric block designs with parameters (41, 16, 6) and (66, 26, 10). J. Combin. Theory, Ser. A, 33, 201–204.

    MATH  Google Scholar 

  • Whiteman, A. L. (1990). A family of D-optimal designs. Ars Combinatoria, 30, 23–26.

    MathSciNet  MATH  Google Scholar 

  • Yang, C. H. (1966a). Some designs for maximal (+1,-1)-determinant of order n E 2mod4. Math. Comp., 20, 147–148.

    MATH  Google Scholar 

  • Yang, C. H. (1966b). A construction of maximal (+1,-1)-matrix of order 54. Bull. Amer. Math. Soc., 72, 293.

    MATH  Google Scholar 

  • Yang, C. H. (1968). On designs of maximal (+1,-1)-matrices of order n E 2mod4. Math. Comp., 22, 174–180.

    MATH  Google Scholar 

  • Yang, C. H. (1969). On designs of maximal (+1,-1)-matrices of order n 2mod4, II. Math. Comp., 23, 201–205.

    MathSciNet  MATH  Google Scholar 

  • Yang, C. H. (1976). Maximal binary matrices and sum of two squares. Math. Comp., 30, 148–153.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, National Technical University of Athens, Zografou, 15773, Athens, Greece

    Christos Koukouvinos

Authors
  1. Christos Koukouvinos
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Statistics, Athens University of Economics and Business, 76 Patission Street, 104-34, GR-Athens, Greece

    Christos P. Kitsos

  2. Department of Statistics, University of Economics and Business Administration, Augasse 2-6, A-1090, Vienna, Austria

    Werner G. Müller

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Koukouvinos, C. (1995). D-Optimal First Order Saturated Designs with n ≡ 2mod4 Observations. In: Kitsos, C.P., Müller, W.G. (eds) MODA4 — Advances in Model-Oriented Data Analysis. Contributions to Statistics. Physica, Heidelberg. https://doi.org/10.1007/978-3-662-12516-8_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-12516-8_14

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-7908-0864-3

  • Online ISBN: 978-3-662-12516-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation