Skip to main content
Log in

What is a design? How should we classify them?

  • Published:
Designs, Codes and Cryptography Aims and scope Submit manuscript

Abstract

Design theory crosses the boundary between mathematics and statistics, and includes a wide range of disparate types of design. In this paper we present a classification scheme which aims to include as many important types as possible, based on a balance among concept, representation and use.

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

References

  • Anderson I (1997). Combinatorial designs and tournaments. Oxford University Press, Oxford

    MATH  Google Scholar 

  • Atkinson AC and Donev AN (1992). Optimum experimental designs. Oxford University Press, Oxford

    MATH  Google Scholar 

  • Bailey RA (1999). Choosing designs for nested blocks. Listy Biometryczne 36: 85–126

    MATH  Google Scholar 

  • Bailey RA (2004). Association schemes: designed experiments, algebra and combinatorics. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Bailey RA, Cameron PJ, Dobcsányi P, Morgan JP and Soicher LH (2006). Designs on the Web. Discrete Math 306: 3014–3027

    Article  MATH  Google Scholar 

  • Bailey RA and Speed TP (1986). Rectangular lattice designs: efficiency factors and analysis. Ann Stat 14: 874–895

    MATH  Google Scholar 

  • Brouwer AE, van Lint JH (1984) Strongly regular graphs and partial geometries. In: Enumeration and design. Academic Press, Toronto, pp 85–122

  • Buekenhout F (1979). Diagrams for geometries and groups. J. Combin Theory (A) 27: 121–151

    Article  MATH  Google Scholar 

  • Cameron PJ (1991) Projective and polar spaces. QMW Maths Notes vol 13. Queen Mary and Westfield College, London. Second edition available at http://www.maths.qmul.ac.uk/∼pjc/pps/

  • Cameron PJ (ed) Encyclopaedia of design theory, http://designtheory.org/library/encyc/

  • Colbourn CJ, Dinitz JH (ed) (1996) Handbook of combinatorial designs, 1st edn. Chapman & Hall/CRC

  • Design Theory Resource Server, http://designtheory.org/

  • Deza M (1992) Perfect matroid designs. In: White N (ed) Matroid applications. Encyc Math Appl vol 40. Cambridge University Press, pp 54–72

  • Eccleston JA and Russell KG (1975). Connectedness and orthogonality in multi-factor designs. Biometrika 62: 341–345

    Article  MATH  Google Scholar 

  • Fisher RA (1942). The theory of confounding in factorial experiments in relation to the theory of groups. Ann Eugen 11: 341–353

    Google Scholar 

  • Hanaki A, Miyamoto I. Classification of association schemes with small vertices, http://kissme.shinshu-u.ac.jp/as/

  • Hughes DR (1962) Combinatorial analysis: t-designs and permutation groups. In: Proceedings of the symposium in pure mathematics 6. American Mathematical Society, Providence, Rhode Island, pp 39–41

  • Hughes DR and Piper FC (1985). Design theory. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • John JA and Williams ER (1995). Cyclic and computer-generated designs. Chapman and Hall, London

    MATH  Google Scholar 

  • Khosrovshahi GB and Tayfeh-Rezaie B (2006). Large sets of t-designs through partitionable sets: a survey. Discrete Math 306: 2993–3004

    Article  MATH  Google Scholar 

  • La Jolla Covering Repository, http://www.ccrwest.org/cover.html

  • Li PC and van Rees GHJ (2002). Lotto design tables. J Combin Designs 10: 335–359

    Article  MATH  Google Scholar 

  • McSorley JP, Phillips NCK, Wallis WD and Yucas JL (2005). Double arrays, triple arrays and balanced grids. Designs, Codes Cryptogr 35: 21–45

    Article  Google Scholar 

  • Morgan JP, Preece DA and Rees DH (2001). Nested balanced incomplete block designs. Discrete Math 231: 351–389

    Article  MATH  Google Scholar 

  • Nelder JA (1968). The combination of information in generally balanced designs. J Roy Stat Soc, Ser B 30: 303–311

    MATH  Google Scholar 

  • Pasini A (1994). Diagram geometries. Oxford University Press, Oxford

    MATH  Google Scholar 

  • Preece DA (1976). Non-orthogonal Graeco-Latin designs. In: Casse, LRA and Wallis, WD (eds) Combinatorial Mathematics IV Lecture Notes in Mathematics, vol 560., pp 7–26. Springer, Berlin

    Chapter  Google Scholar 

  • Preece DA (1990). Fifty years of Youden squares: a review. Bull Inst Math Appl 26: 65–75

    MATH  Google Scholar 

  • Preece DA and Phillips NCK (1997). A new type of Freeman-Youden rectangle. J Combin Math Combin Comput 25: 65–78

    MATH  Google Scholar 

  • Pukelsheim F (1993). Optimal design of experiments. Wiley, New York

    MATH  Google Scholar 

  • Shah KR and Sinha BK (1989). Theory of optimal designs. Springer, New York

    MATH  Google Scholar 

  • Soicher LH SOMA Update, http://www.maths.qmul.ac.uk/∼leonard/soma/

  • Tits J (1974). Buildings of spherical type and finite BN-pairs. Lecture Notes in Math vol 382. Springer-Verlag, Berlin

    Google Scholar 

  • Williams ER, Patterson HD and John JA (1976). Resolvable designs with two replications. J Roy Stat Soc, Ser B 38: 296–301

    MATH  Google Scholar 

  • Yates F (1935) Complex experiments. J Roy Stat Soc, Suppl 2:181–247

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to R. A. Bailey.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bailey, R.A., Cameron, P.J. What is a design? How should we classify them?. Des. Codes Cryptogr. 44, 223–238 (2007). https://doi.org/10.1007/s10623-007-9092-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10623-007-9092-3

Keywords

AMS Classification

Navigation