Designs, Codes and Cryptography

, Volume 35, Issue 1, pp 21–45 | Cite as

Double Arrays, Triple Arrays and Balanced Grids

  • John P. McsorleyEmail author
  • N. C. K. Phillips
  • W. D. Wallis
  • J. L. Yucas


Triple arrays are a class of designs introduced by Agrawal in 1966 for two-way elimination of heterogeneity in experiments. In this paper we investigate their existence and their connection to other classes of designs, including balanced incomplete block designs and balanced grids.


block design array 


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  1. Agrawal, H. 1966Some methods of construction of designs for two-way elimination of heterogeneityJ.Am.Statist.Assoc.6111531171Google Scholar
  2. Agrawal, H.L., Mishra, R.I. 1971Some methods of construction of (4DIB) designsCalcutta Statist. Assoc. Bull.208992zbMATHGoogle Scholar
  3. Bhattacharya, K.N. 1944A new balanced incomplete block designSci.Cult.9508Google Scholar
  4. Bruck, R.H., Ryser, H.J. 1949The non-existence of certain finite projective planesCan.J.Math.18893zbMATHMathSciNetGoogle Scholar
  5. Chowla, S., Ryser, H.J. 1950Combinatorial problemsCan. J. Math.29399zbMATHMathSciNetGoogle Scholar
  6. Hall, M., Connor, W.S. 1954An embedding theorem for balanced incomplete block designsCan. J. Math.63541zbMATHMathSciNetGoogle Scholar
  7. Metsch, A. 1995Quasi-residual designs, (1half)-designs, and strongly regular multigraphsDiscrete Math.143167188zbMATHMathSciNetGoogle Scholar
  8. Neumaier, K. 1982Quasi-residual 2-designs, (1half)-designs, and strongly regular multigraphsGeom. Dedicata12351366zbMATHMathSciNetGoogle Scholar
  9. Potthoff, R.F. 1962Three-factor additive designs more general than the Latin squareTechnometrics4187208zbMATHMathSciNetGoogle Scholar
  10. Preece, D.A. 1966Some row and column designs for two sets of treatmentsBiometrics22125MathSciNetGoogle Scholar
  11. D. A. Preece, Non-orthogonal graeco-latin designs.Combinatorial Mathematics IV, In Proc of the 4th Australian Conference Springer-Verlag (1976), pp. 7–26.Google Scholar
  12. Raghavarao, D., Nageswarerao, G. 1974A note on a method of construction of designs for two-way elimination of heterogeneityCommun. Statist.3197199CrossRefGoogle Scholar
  13. Schutzenberger, M.P. 1949A non-existence theorem for an infinite family of symmetrical block designsAnn. Eugen14286287MathSciNetGoogle Scholar
  14. Singhi, N.M., Shrikhande, S.S. 1973Embedding of quasi-residual designs with (l = 3)Utilitas Math43553zbMATHMathSciNetGoogle Scholar
  15. Singhi, N.M., Shrikhande, S.S. 1974Embedding of quasi-residual designsGeom. Ded.2509517zbMATHMathSciNetGoogle Scholar
  16. Smith, C.A.B., Hartley, H.O. 1948The construction of Youden squaresJ. R. Statist. Soc.Ser. B10262263zbMATHMathSciNetGoogle Scholar
  17. Stanton, R.G. 1969Interconnections of related BIBDsJ. Comb. Theory6387391zbMATHGoogle Scholar
  18. J. H. van Lint, V. D. Tonchev and I. N. Landgev, A new design.Coding Theory and Design Theory Part II Design Theory, IMA Math. Appl. Springer-Verlag, Vol. 14 (1990) pp. 251–256.Google Scholar
  19. W. D. Wallis,Combinatorial Designs, Marcel Dekker, New York, (1988).Google Scholar
  20. W. D. Wallis and J. L. Yucas, Note on the construction of designs for the elimination of heterogeneity,J. Comb. Math. Comb. Comput., (to appear).Google Scholar
  21. Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • John P. Mcsorley
    • 1
    Email author
  • N. C. K. Phillips
    • 2
  • W. D. Wallis
    • 1
  • J. L. Yucas
    • 1
  1. 1.Department of MathematicsSouthern Illinois UniversityCarbondaleUSA
  2. 2.Department of Computer ScienceSouthern Illinois UniversityCarbondaleUSA

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