Skip to main content
Log in

Procedimenti per la costruzione di piani di esperimenti incompleti

  • Published:
CALCOLO Aims and scope Submit manuscript

Abstract

Two new methods for the construction of partially balanced incomplete block designs with two associate classes are reported. The first method concerns triangular designs and the second one cyclic designs. Some designs are obtained which have not previously been published. Furthermore, the first results of a systematic search of cyclic designs using a digital computer are illustrated.

Riassunto

Si illustrano due nuovi procedimenti di costruzione di piani di esperimenti incompleti a due classi: il primo riguarda i piani triangolari, il secondo i piani ciclici. Si ottengono così piani, alcuni dei quali non figurano negli elenchi fin'ora pubblicati. Si espongono inoltre i primi risultati di una ricerca sistematica, compiuta con un programma di calcolo per un elaboratore elettronico, di piani ciclici a due classi.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Bibliografia

  • Andree, R. V.A Table of indices and power residues for all primes and prime powers below 2000, W. W. Norton e Company, New York, (1962).

    MATH  Google Scholar 

  • Clatworthy, W. H.Contribution on partially balanced incomplete block designs with two associate classes, National Bureau of Standards, Washington—Applied Mathematics Series—n0 17, (1956).

    Google Scholar 

  • Cochran, W. G.-Cox, G. M.Experimental designs, J. Wiley e Sons, New York, II Ed., (1957).

    MATH  Google Scholar 

  • Gassner, B. J.Cyclic BIB designs, «1965 IEEE International Convention Record», Part. 7: Cricnit Theory; Information Theory; Basic Science; Electrostatic Processes—259–277.

  • Hall, M.Block design, in «Applied Combinatorial Mathematics» (Ed E. F. Beckenbach), J. Wiley e Sons, New York, (1964), 369–405.

    Google Scholar 

  • Lehmer, E.On residue difference sets, Canadian Journal of Mathematics,5, (1953), 425–432.

    MATH  MathSciNet  Google Scholar 

  • Lunelli, L.Codici binari a peso costante, Calcolo, 1, 2, (1964), 155–187.

    MATH  MathSciNet  Google Scholar 

  • Mann, H. B.Analysis and designs of experiments, Dover, New York, (1949).

    Google Scholar 

  • Mann, H. B.Addition theorems: The addition theorems of group theory and number theory, Interscience Publishers—J. Wiley e Sons, New York, (1965).

    MATH  Google Scholar 

  • Masuyama, M.Construction cyclique de blocs incomplets partiellement equilibrés, Relazione alla «Ecole d'Eté de I'OTAN sur les Méthodes Combinatoires en Theorie de l'Information et du Codage» (Royan: 26 agosto—8 settembre 1965).

  • Ryser, F. M.Combinational Mathematics, J. Wiley e Sons, New York, (1963).

    Google Scholar 

  • Sprott, D. A.Some series of partially balanced incomplete block designs, Canadian Journal of Mathematics7, (1955), 369–381.

    MATH  MathSciNet  Google Scholar 

  • Vinogradov, I. M.Elements of number theory (1949), Trad. dal russo di S. Kravetz, Dover Publications, (1954).

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lunelli, L. Procedimenti per la costruzione di piani di esperimenti incompleti. Calcolo 2, 313–338 (1965). https://doi.org/10.1007/BF02576707

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02576707

Navigation