Encyclopaedia of DesignTheory: Bibliography

Books | Lecture notes | Papers | Web resources

This page gives a (necessarily incomplete) list of references on design theory. For a much wider list of Web resources, see the Design Resources page.


  1. I. Anderson, Combinatorial Designs and Tournaments, Oxford University Press, Oxford, 1997.
  2. M. Aschbacher, Finite group theory, Cambridge University Press, Cambridge, 1994.
  3. E. F. Assmus Jr and J. D. Key, Codes and Finite Geometries, Cambridge University Press, Cambridge, 1992: Web page
  4. R. A. Bailey, Association Schemes: Designed Experiments, Algebra and Combinatorics, Cambridge Studies in Applied Mathematics, Cambridge University Press, Cambridge, 2004: Web page
  5. E. Bannai and T. Ito, Algebraic Combinatorics I: Association Schemes, Benjamin, New York, 1984.
  6. Lowell Beineke and Robin Wilson (eds.), Topics in Algebraic Graph Theory Cambridge Univ. Press, Cambridge, 2004.
  7. T. Beth, D. Jungnickel and H. Lenz, Design Theory (2 volumes), Cambridge University Press, Cambridge, 1999.
  8. N. L. Biggs, Discrete Mathematics (2nd edition), Oxford University Press, Oxford, 2002.
  9. A. E. Brouwer, A. M. Cohen and A. Neumaier, Distance-regular Graphs, Springer, Berlin, 1989.
  10. K. S. Brown, Buildings, Springer, New York, 1989.
  11. F. Buekenhout (editor), Handbook of Incidence Geometry, North-Holland, Amsterdam, 1995.
  12. T. Calinski and S. Kageyama, Block Designs: A Randomization Approach, Lecture Notes in Statistics 150, Springer, New York, 2000.
  13. P. J. Cameron, Permutation Groups, Cambridge University Press, Cambridge, 1999: Web page
  14. P. J. Cameron and J. H. van Lint, Designs, Graphs, Codes and their Links, Cambridge University Press, Cambridge, 1991.
  15. R. W. Carter, Simple Groups of Lie Type, Wiley Interscience, New York, 1972.
  16. W. G. Cochran and G. M. Cox, Experimental Designs, Wiley, New York, 1950.
  17. C. Colbourn and J. Dinitz (editors), The Handbook of Combinatorial Design, CRC Press, 1996: Web page
  18. G. M. Constantine, Combinatorial Theory and Statistical Design, Wiley, New York, 1987.
  19. J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, and R. A. Wilson, An ATLAS of Finite Groups, Oxford University Press, Oxford, 1985.
  20. D. R. Cox, Planning of Experiments, Wiley, New York, 1958.
  21. B. A. Davey and H. A. Priestley, Introduction to Lattices and Order, Cambridge University Press, Cambridge, 1990.
  22. P. Dembowski, Finite Geometries, Springer, Berlin, 1968.
  23. J. Dénes and A. D. Keedwell, Latin squares and their applications, Akademiai Kiado, Budapest, 1974.
  24. J. Dénes and A. D. Keedwell (editors), Latin squares: New developments in the theory and applications, Annals of Discrete Mathematics, 46, North-Holland, Amsterdam, 1991.
  25. A. Dey, Theory of Block Designs, Wiley Eastern, New Delhi, 1986.
  26. J. H. Dinitz and D. R. Stinson (editors), Contemporary Design Theory: A Collection of Surveys, Wiley, New York, 1992.
  27. D. J. Finney, An Introduction to the Theory of Experimental Design, University of Chicago Press, Chicago, 1960.
  28. R. A. Fisher, The Design of Experiments, Oliver and Boyd, Edinburgh, 1935.
  29. J. A. Gallian, Contemporary Abstract Algebra, Houghton Mifflin, Boston, 1998.
  30. A. V. Geramita and Jennifer Seberry, Orthogonal Designs: Quadratic forms and Hadamard matrices, Marcel Dekker, New York - Basel, 1979.
  31. C. D. Godsil, Algebraic combinatorics, Chapman & Hall, New York, 1993.
  32. D. Gorenstein, Finite Simple Groups: An Introduction to their Classification, Plenum Press, New York, 1982.
  33. R. L. Graham, M. Grötschel and L. Lovász (editors), Handbook of Combinatorics, North-Holland, Amsterdam, 1995.
  34. Charles M. Grinstead and J. Laurie Snell, Introduction to Probability (Web-based book)
  35. M. Hall Jr., Combinatorial Theory, Wiley, New York, 1986.
  36. A. S. Hedayat, N. J. A. Sloane and John Stufken, Orthogonal Arrays: Theory and Applications, Springer, Berlin, 1999: Web page
  37. R. Hill, A First Course in Coding Theory, Oxford University Press, Oxford, 1986.
  38. J. W. P. Hirschfeld, Projective Geometries over Finite Fields (second edition), Oxford University Press, Oxford, 1998: Web page
  39. J. W. P. Hirschfeld, Finite Projective Spaces of Three Dimensions, Oxford University Press, Oxford, 1985.
  40. J. W. P. Hirschfeld and J. A. Thas, General Galois Geometries, Oxford University Press, Oxford, 1991.
  41. D. R. Hughes and F. C. Piper, Design Theory, Cambridge University Press, Cambridge, 1985.
  42. J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge Univ. Press, Cambridge, 1990.
  43. Y. Ionin and M. Shrikhande, Combinatorics of Symmetric Designs, Cambridge Univ. Press, Cambridge, 2006.
  44. J. A. John, Cyclic Designs, Chapman and Hall, London, 1987.
  45. O. Kempthorne, Design and Analysis of Experiments, Wiley, New York, 1952.
  46. R. Lidl and H. Niederreiter, Finite Fields, Cambridge University Press, Cambridge, 1996.
  47. C. C. Lindner and A. Rosa (editors), Topics in Steiner systems, Ann. Discrete Math. 7, Elsevier, Amsterdam, 1979.
  48. J. H. van Lint, Introduction to Coding Theory, Springer, New York, 1982.
  49. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, North-Holland, Amsterdam, 1977.
  50. J. D. Malley, Optimal Unbiased Estimation of Variance Components, Lecture Notes in Statistics 39, Springer, Berlin, 1986.
  51. A. Pasini, Diagram Geometries, Oxford University Press, Oxford, 1994.
  52. V. Pless, Introduction to the Theory of Error-correcting Codes, Wiley, New York, 1982.
  53. D. Raghavarao, Constructions and Combinatorial Problems in Design of Experiments, Wiley, New York, 1971.
  54. M. A. Ronan, Lectures on Buildings, Academic Press, Boston, 1989.
  55. K. R. Shah and B. K. Sinha, Theory of Optimal Designs, Springer, New York, 1989.
  56. M. S. Shrikhande and S. S. Sane, Quasi-symmetric designs, London Mathematical Society Lecture Note Series 164, Cambridge University Press, Cambridge, 1991.
  57. A. P. Street and D. J. Street, Combinatorics of Experimental Design, Oxford University Press, Oxford, 1987.
  58. J. Talbot and D. Welsh, Complexity and Cryptography, Cambridge University Press, 2006.
  59. J. Tits, Buildings of Spherical Type and Finite BN-Pairs, Springer, Berlin, 1974.
  60. W.D. Wallis, Anne Penfold Street and Jennifer Seberry Wallis, Combinatorics : Room Squares, Sum-free Sets, Hadamard Matrices, Lecture Notes in Mathematicsi 292, Springer-Verlag, Berlin-Heidelberg-New York, 1972, 508 pages.
  61. D. J. A. Welsh, Matroid Theory, Academic Press, London, 1976.
  62. D. J. A. Welsh, Codes and Cryptography, Oxford University Press, Oxford, 1988.

Lecture notes on the Web EXTERNAL

  1. Ian Anderson and Iiro Honkala, A short course on combinatorial designs
  2. R. A. Bailey, Notes on designing an experiment
  3. Francis Buekenhout, History and prehistory of polar spaces and of generalized quadrangles
  4. Peter J. Cameron, Finite geometry and coding theory
  5. Peter J. Cameron, Classical groups
  6. Peter J. Cameron, Projective and polar spaces
  7. Peter J. Cameron, Polynomial aspects of codes, matroids and permutation groups
  8. J. Eisfeld and L. Storme, (Partial) t-spreads and minimal t-covers in finite projective spaces
  9. Willem H. Haemers, Matrix techniques for strongly regular graphs and related geometries
  10. J. I. Hall, Notes on coding theory
  11. Steven R. Pagano, Matroids and signed graphs
  12. J. A. Thas and H. Van Maldeghem, Embeddings of geometries in finite projective spaces


  1. P. Alejandro, R. A. Bailey and P. J. Cameron, Association schemes and permutation groups, Discrete Math. 266 (2003), 47-67.
  2. L. D. Andersen and A. J. W. Hilton, Thank Evans!, Proc. London Math. Soc. (3) 47 (1983), 507-522.
  3. L. Babai, Almost all Steiner triple systems are asymmetric, in Topics in Steiner systems (ed. C. C. Lindner and A. Rosa), Ann. Discrete Math. 7, Elsevier, Amsterdam, 1979, pp. 37-39.
  4. R. A. Bailey, Latin squares with highly transitive automorphism groups, J. Austral. Math. Soc. (A) 33 (1982), 18-22.
  5. R. A. Bailey, Designs: mappings between structured sets, pp. 22--51 in Surveys in Combinatorics, 1989 (ed. J. Siemons), Cambridge Univ. Press, Cambridge, 1989.
  6. R. A. Bailey, Strata for randomized experiments (with discussion), J. Royal Statistical Society Series B 53 (1991), 27-78.
  7. R. A. Bailey, Orthogonal partitions in designed experiments, Designs, Codes and Cryptography 8 (1996), 45-77.
  8. R. A. Bailey, Resolved designs viewed as sets of partitions, pp. 17-47 in Combinatorial Designs and their Applications (ed. F. C. Holroyd, K. A. S. Quinn, C. Rowley and B. S. Webb), Chapman & Hall/CRC Press Research Notes in Mathematics 403, CRC Press, Boca Raton, 1999.
  9. R. A. Bailey, Suprema and infima of association schemes, Discrete Math. 248 (2002), 1-16.
  10. R. A. Bailey: Balanced colourings of strongly regular graphs. Discrete Mathematics, 293 (2005), 73-90.
  11. K. Balasubramanian, On transversals in Latin squares, Linear Algebra Appl. 131 (1990), 125-129.
  12. E. Bannai, An introduction to association schemes, pp. 1-70 in Methods of Discrete Mathematics (ed. S.Löwe, F. Mazzocca, N. Melone and U. Ott), Quaderni di Mathematica 5, Seconda Università di Napoli, Napoli, 1999.
  13. R. C. Bose, On some new series of balanced incomplete block designs, Bull. Calcutta Math. Soc. 34 (1942), 17-31.
  14. R. C. Bose and K. R. Nair, Partially balanced incomplete block designs, Sankhya 4 (1939), 337-372.
  15. R. C. Bose and J. N. Srivastava, On a bound useful in the theory of factorial design and error-correcting codes, Ann. Math. Statist. 35 (1964), 408-414.
  16. F. Buekenhout, Diagrams for geometries and groups, J. Combinatorial Theory (A) 27 (1979), 121-151.
  17. P. J. Cameron, Cycle index, weight enumerator and Tutte polynomial, Electronic J. Combinatorics 9 (2002), #N2 (10pp), available from http://www.combinatorics.org.
  18. P. J. Cameron and C. E. Praeger, Block-transitive t-designs, I: point-imprimitive designs, Discrete Math. 118 (1993), 33--43; II, large t, pp. 103-119 in Finite Geometry and Combinatorics (ed. A. Beutelspacher et al.), Cambridge University Press, Cambridge, 1993.
  19. M. C. Chakrabarti, On the C-matrix in design of experiments, J. Indian Statist. Assoc. 1 (1963), 8-23.
  20. Ph. Delsarte, An algebraic approach to the association schemes of coding theory, Philips Research Reports Suppl. 10 (1973).
  21. A. Dey, M. Singh and G. M. Saha, Efficiency balanced block designs, Commun. Statist. (A) 10 (1981), 237-247.
  22. M.~Deza, Perfect matroid designs, Encyclopedia of Mathematics and its Applications 40 (1992), 54-72.
  23. J. Doyen and R. M. Wilson, Embeddings of Steiner triple systems, Discrete Math. 5 (1973), 229-239.
  24. R. A. Fisher, An examination of the different possible solutions of a problem in incomplete blocks, Ann. Eugenics 10 (1940), 52-75.
  25. C. D. Godsil and B. D. McKay, Asymptotic enumeration of Latin rectangles, J. Combinatorial Theory (B) 48 (1990), 19-44.
  26. R. Häggkvist and J. C. M. Janssen, All-even latin squares, Discrete Math. 157 (1996), 199-206.
  27. M. Hall, Jr., Automorphisms of Steiner triple systems, IBM J. Research Develop. 4 (1960), 460-472.
  28. M. Hall, Jr., Note on the Mathieu group M12, Arch. Math. 13 (1962), 334-340.
  29. D. G. Higman, Coherent algebras, Linear Algebra Appl. 93 (1987), 209-239.
  30. A. A. Ivanov, Distance-transitive graphs and their classification, pp. 283-378 in Investigations in the Algebraic Theory of Combinatorial Objects (ed. I. A. Faradzev, A. A. Ivanov, M. H. Klin and A. J. Woldar), Kluwer, Dordrecht, 1994.
  31. M. T. Jacobson and P. Matthews, Generating uniformly distributed random Latin squares, J. Combinatorial Design 4 (1996), 405-437.
  32. M. R. Jerrum, Computational Pólya theory, pp. 103-118 in Surveys in Combinatorics, 1995 (Peter Rowlinson, ed.), London Math. Soc. Lecture Notes 218, Cambridge University Press, Cambridge, 1995.
  33. P. Kaski and P. R. J. Östergård, The Steiner triple systems of order 19, Math. Comp. 73 (2004), 2075-2092.
  34. J. H. van Lint, Block designs with repeated blocks and (b,r,lambda)=1, J. Combinatorial Theory (A) 15 (1973), 288-309.
  35. B. D. McKay and I. M. Wanless, Most Latin squares have many subsquares, J. Combinatorial Theory (A) 86 (1999), 323-347.
  36. B. D. McKay and I. M. Wanless, On the number of Latin squares, Ann. Combin. 9 (2005), 335-344.
  37. E. H. Moore, Tactical memoranda, Amer. J. Math. 18 (1896), 264-303.
  38. P. M. Neumann and C. E. Praeger, An inequality for tactical configurations, Bull. London Math. Soc. 28 (1996), 471-475.
  39. D. A. Preece, Orthogonality and designs: a terminological muddle, Utilitas Math. 12 (1977), 201-223.
  40. D. A. Preece, Balance and designs: Another terminological tangle, Utilitas Math. 21C (1982), 85-186; correction, ibid. 23 (1983), 347.
  41. D. A. Preece, Fifty years of Youden squares: a review, Bull. Inst. Math. Appl. 26 (1990), 65-75.
  42. D. A. Preece, Balanced Ouchterlony neighbour designs and quasi Rees neighbour designs, J. Combinatorial Mathematics and Combinatorial Computing 15 (1994), 197--219.
  43. V. R. Rao, A note on balanced designs, Ann. Math. Statist. 29 (1958), 290-294.
  44. D. K. Ray-Chaudhuri and R. M. Wilson, Solution of Kirkman's schoolgirl problem, Combinatorics, Proc. Symp. Pure Math. 19, 187-203 (1971).
  45. G.-C. Rota, On the foundations of combinatorial theory, I: Theory of Möbius functions, Z. Wahrscheinlichkeitstheorie 2 (1964), 340-368.
  46. H. J. Ryser, A combinatorial theorem with an application to latin rectangles, Proc. Amer. Math. Soc. 2 (1951), 550-552.
  47. J. Seberry and M. Yamada, Hadamard matrices, sequences and block designs, pp. 431-560 in Contemporary Design Theory: A Collection of Surveys (ed. J. H. Dinitz and D. R. Stinson), Wiley, New York, 1992.
  48. J. J. Seidel, Strongly regular graphs of L2-type and of triangular type, Proc. Kon. Nederl. Akad. Wetensch. Ser. A 70 (= Indag. Math. 29) (1967), 188-196.
  49. J. J. Seidel, Strongly regular graphs with (-1,1,0) adjacency matrix having eigenvalue 3, Linear Algebra Appl. 1 (1968), 281-298.
  50. J. J. Seidel, A survey of two-graphs, pp. 481--511 in Proc. Internat. Coll. Teorie Combinatorie (Roma 1973), Accad. Naz. Lincei, Roma, 1977.
  51. B. Smetaniuk, A new construction on latin squares, I: A proof of the Evans conjecture, Ars Combinatoria 9 (1981), 155-172.
  52. T. P. Speed and R. A. Bailey, On a class of association schemes derived from lattices of equivalence relations, pp. 55-74 in Algebraic Structures and Applications (ed. P. Schultz, C. E. Praeger and R. P. Sullivan), Marcel Dekker, New York, 1982.
  53. W. D. Wallis, Construction of strongly regular graphs using affine designs, Bull. Austral. Math. Soc. 4 (1971), 41-49.
  54. R. M. Wilson, Non-isomorphic Steiner triple systems, Math. Z. 135 (1974), 303-313.
  55. R. M. Wilson, An existence theory for pairwise balanced designs: I, Composition theorems and morphisms, J. Combinatorial Theory (A) 13 (1972), 220-245; II, The structure of PBD-closed sets and the existence conjectures, ibid. 13 (1972), 246-273; III, A proof of the existence conjectures, ibid. 18 (1975), 71-79.
  56. R. M. Wilson, Construction and uses of pairwise balanced designs, Mathematical Centre Tracts 55, Mathematisch Centrum, Amsterdam, 1974.
  57. P.-H. Zieschang, Homogeneous coherent configurations as generalized groups and their relationship to buildings, J. Algebra 178 (1995), 677-709.

Other Web resources EXTERNAL

  1. 100 years of design theory in Biometrika: an annotated bibliography by A. C. Atkinson and R. A. Bailey
  2. Semi-Latin squares page (maintained by R. A. Bailey)
  3. Neighbour-balanced designs page (maintained by R. A. Bailey)
  4. Collected papers of R. A. Fisher at the University of Adelaide (maintained by J. H. Bennett)
  5. Fractional factorial design generator by Marko Boon
  6. Permutation groups resources (maintained by Peter J. Cameron)
  7. Hyperoval Page (maintained by Bill Cherowitzo)
  8. Flocks of Cones (maintained by Bill Cherowitzo)
  9. Design Links (maintained by Jeff Dinitz)
  10. Design and Analysis of Experiments at the Horticultural Research Institute (maintained by Rodney N. Edmondson)
  11. La Jolla Covering Repository (maintained by Dan Gordon)
  12. Small association schemes (maintained by A. Hanaki)
  13. Matroids page (maintained by Sandra Kingan)
  14. History of Statistics at the University of York (maintained by Peter M. Lee)
  15. Design Computing (software, courses, consulting, research) by Nam-Ky Nguyen
  16. Jennie Seberry's libraries of Hadamard and other matrices, and designs of various types
  17. Virtual Laboratories in Probability and Statistics (maintained by Kyle Siegrist)
  18. Library of Orthogonal Arrays (maintained by Neil Sloane)
  19. Partial Spreads page (maintained by Leonard Soicher)
  20. SOMAs page (maintained by Leonard Soicher)
  21. Ted Spence's files: designs, strongly regular graphs, Hadamard matrices, etc.
  22. Matroid Miscellany (maintained by Thomas Zaslavsky)

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Peter J. Cameron
13 March 2006