Continuing in the bestselling, informative tradition of the first edition, the Handbook of Combinatorial Designs, Second Edition remains the only resource to contain all of the most important results and tables in the field of combinatorial design. This handbook covers the constructions, properties, and applications of designs as well as existence

chapter |2 pages

Part I: Introduction

chapter 1|8 pages

Opening the Door

ByCharles J. Colbourn

chapter 2|12 pages

Design Theory: Antiquity to 1950

chapter |2 pages

Part II: Block Designs

chapter 1|33 pages

2-(v, k, λ) Designs of Small Order

ByRudolf Mathon, Alexander Rosa

chapter 2|14 pages

Triple Systems

ByCharles J. Colbourn

chapter 3|7 pages

BIBDs with Small Block Size

ByR. Julian R. Abel, Malcolm Greig

chapter 5|8 pages

Steiner Systems

ByCharles J. Colbourn, Rudolf Mathon

chapter 6|14 pages

Symmetric Designs

ByYury J. Ionin, Tran van Trung

chapter 7|9 pages

Resolvable and Near-Resolvable Designs

ByR. Julian R. Abel, Gennian Ge, Jianxing Yin

chapter |2 pages

Part III: Latin Squares

chapter 1|17 pages

Latin Squares

ByCharles J. Colbourn, Jeffrey H. Dinitz, Ian M. Wanless

chapter 2|8 pages


ByFrank E. Bennett, Charles C. Lindner

chapter 3|33 pages

Mutually Orthogonal Latin Squares (MOLS)

ByR. Julian R. Abel, Charles J. Colbourn, Jeffrey H. Dinitz

chapter 4|18 pages

Incomplete MOLS

ByR. Julian R. Abel, Charles J. Colbourn, Jeffrey H. Dinitz

chapter 5|8 pages

Self-Orthogonal Latin Squares (SOLS)

ByNorman J. Finizio, L. Zhu

chapter 6|5 pages

Orthogonal Arrays of Index More Than One

ByMalcolm Greig, Charles J. Colbourn

chapter 7|5 pages

Orthogonal Arrays of Strength More Than Two

ByCharles J. Colbourn

chapter |2 pages

Part IV: Pairwise Balanced Designs

chapter 1|5 pages

PBDs and GDDs: The Basics

ByRonald C. Mullin, Hans-Dietrich O. F. Gronau

chapter 2|11 pages

PBDs: Recursive Constructions

ByMalcolm Greig, Ronald C. Mullin

chapter 3|8 pages


ByR. Julian R. Abel, Frank E. Bennett, Malcolm Greig

chapter 4|6 pages

Group Divisible Designs

ByGennian Ge

chapter 5|5 pages

PBDs, Frames, and Resolvability

ByGennian Ge, Ying Miao

chapter 6|5 pages

Pairwise Balanced Designs as Linear Spaces

ByAnton Betten

chapter 1|7 pages

Hadamard Matrices and Hadamard Designs

ByRobert Craigen, Hadi Kharaghani

chapter 2|16 pages

Orthogonal Designs

ByRobert Craigen, Hadi Kharaghani

chapter 3|3 pages

D-Optimal Matrices

ByHadi Kharaghani, William Orrick

chapter 4|2 pages

Bhaskar Rao Designs

ByWarwick de Launey

chapter 5|5 pages

Generalized Hadamard Matrices

ByWarwick de Launey

chapter 6|7 pages

Balanced Generalized Weighing Matrices and Conference Matrices

ByYury J. Ionin, Hadi Kharaghani

chapter 7|4 pages

Sequence Correlation Tor Helleseth

chapter 8|4 pages

Complementary, Base, and Turyn Sequences

ByHadi Kharaghani, Christos Koukouvinos

chapter 9|2 pages

Optical Orthogonal Codes Tor Helleseth

chapter |2 pages

Part VI: Other Combinatorial Designs

chapter 1|5 pages

Association Schemes

ByChristopher D. Godsil, Sung Y. Song

chapter 2|3 pages

Balanced Ternary Designs

BySpencer P. Hurd, Dinesh G. Sarvate

chapter 3|4 pages

Balanced Tournament Designs

ByEsther R. Lamken

chapter 4|2 pages

Bent Functions

ByDouglas R. Stinson

chapter 5|6 pages

Block-Transitive Designs

ByAnne Delandtsheer

chapter 6|8 pages

Complete Mappings and Sequencings of Finite Groups

ByAnthony B. Evans

chapter 7|2 pages


ByHarald Gropp

chapter 8|2 pages

Correlation-immune and Resilient Functions

ByK. Gopalakrishnan, Douglas R. Stinson

chapter 9|4 pages

Costas Arrays

ByHerbert Taylor, Jeffrey H. Dinitz

chapter 10|4 pages

Covering Arrays

ByCharles J. Colbourn

chapter 11|8 pages


ByDaniel M. Gordon, Douglas R. Stinson

chapter 12|9 pages

Cycle Decompositions

ByDarryn Bryant, Chris Rodger

chapter 13|3 pages

13Defining Sets

ByKen Gray, Anne Penfold Street

chapter 14|4 pages

14Deletion-correcting Codes

ByVladimir I. Levenshtein

chapter 15|3 pages


ByK. Gopalakrishnan, Douglas R. Stinson

chapter 16|19 pages

16Difference Families

ByR. Julian R. Abel, Marco Buratti

chapter 17|8 pages

17Difference Matrices

ByCharles J. Colbourn

chapter 18|17 pages

18Difference Sets

ByDieter Jungnickel, Alexander Pott, Ken W. Smith

chapter 19|5 pages

19Difference Triangle Sets

ByJames B. Shearer

chapter 20|4 pages

20Directed Designs

ByFrank E. Bennett, Alireza Mahmoodi

chapter 21|20 pages

Factorial Designs

ByDeborah J. Street

chapter 22|7 pages

Frequency Squares and Hypercubes

ByCharles F. Laywine, Gary L. Mullen

chapter 23|5 pages

23Generalized Quadrangles

ByStanley E. Payne

chapter 24|9 pages

24Graph Decompositions

ByDarryn Bryant, Saad El-Zanati

chapter 26|4 pages

26Graphical Designs

ByYeow Meng Chee, Donald L. Kreher

chapter 27|2 pages


ByJean-Claude Bermond, David Coudert

chapter 28|3 pages

28Hall Triple Systems Lucien Be´ne´teau

chapter 29|5 pages

29Howell Designs

ByJeffrey H. Dinitz

chapter 30|2 pages

Infinite Designs

ByPeter J. Cameron, Bridget S. Webb

chapter 31|6 pages

Linear Spaces: Geometric Aspects

ByLynn Margaret Batten

chapter 32|7 pages

Lotto Designs

By(Ben) P. C. Li, G. H. John van Rees

chapter 33|5 pages

Low Density Parity Check Codes

ByIan F. Blake

chapter 34|4 pages

34Magic Squares

ByJoseph M. Kudrle, Sarah B. Menard

chapter 35|7 pages

35Mendelsohn Designs

ByEric Mendelsohn

chapter 36|5 pages

36Nested Designs

ByJ. P. Morgan

chapter 37|3 pages

37Optimality and Efficiency: Comparing Block Designs

ByDeborah J. Street

chapter 38|4 pages

38Ordered Designs, Perpendicular Arrays, and Permutation Sets

ByJu¨rgen Bierbrauer

chapter 39|3 pages

39Orthogonal Main Effect Plans

ByDeborah J. Street

chapter 40|7 pages


ByDouglas R. Stinson, Ruizhong Wei, Jianxing Yin

chapter 41|5 pages

Partial Geometries

ByJoseph A. Thas

chapter 42|4 pages

Partially Balanced Incomplete Block Designs

ByDeborah J. Street, Anne Penfold Street

chapter 43|2 pages

Perfect Hash Families

ByRobert A. Walker II, Charles J. Colbourn

chapter 44|4 pages

Permutation Codes and Arrays

ByPeter J. Dukes

chapter 45|2 pages

Permutation Polynomials

ByGary L. Mullen

chapter 46|2 pages

Pooling Designs

ByDavid C. Torney

chapter 47|2 pages

47Quasi-3 Designs Gary McGuire

chapter 48|6 pages

48Quasi-Symmetric Designs

ByMohan S. Shrikhande

chapter 50|7 pages

Room Squares

ByJeffrey H. Dinitz

chapter 51|15 pages

Scheduling a Tournament

ByJ. H. Dinitz, Dalibor Froncek, Esther R. Lamken, Walter D. Wallis

chapter 52|6 pages

Secrecy and Authentication Codes

ByK. Gopalakrishnan, Douglas R. Stinson

chapter 53|5 pages

Skolem and Langford Sequences

ByNabil Shalaby

chapter 54|5 pages

Spherical Designs

ByAkihiro Munemasa

chapter 55|7 pages


ByJeffrey H. Dinitz

chapter 56|4 pages

Superimposed Codes and Combinatorial Group Testing

ByCharles J. Colbourn, Frank K. Hwang

chapter 57|2 pages

Supersimple Designs

ByHans-Dietrich O. F. Gronau

chapter 58|4 pages

Threshold and Ramp Schemes

ByK. Gopalakrishnan, Douglas R. Stinson

chapter 59|5 pages


ByWilliam J. Martin

chapter 60|5 pages


ByA. S. Hedayat, Gholamreza B. Khosrovshahi

chapter 61|3 pages

Tura´n Systems

ByMiklo´s Ruszinko´

chapter 62|5 pages

Tuscan Squares

ByWensong Chu, Solomon W. Golomb, Hong-Yeop Song

chapter 63|6 pages

t-Wise Balanced Designs

ByEarl S. Kramer, Donald L. Kreher

chapter 64|5 pages

64Whist Tournaments

ByIan Anderson, Norman J. Finizio

chapter 65|7 pages

65Youden Squares and Generalized Youden Designs

ByDonald A. Preece, Charles J. Colbourn

chapter |2 pages

Part VII: Related Mathematics

chapter 1|25 pages


ByVladimir D. Tonchev

chapter 2|27 pages

Finite Geometry

ByLeo Storme

chapter 3|2 pages

Divisible Semiplanes

ByRudolf Mathon

chapter 4|9 pages

Graphs and Multigraphs

ByGordon F. Royle

chapter 5|15 pages

Factorizations of Graphs

ByLars D. Andersen

chapter 6|28 pages

Computational Methods in Design Theory

ByPeter B. Gibbons, Patric R. J. O¨sterg˚ard

chapter 7|8 pages

Linear Algebra and Designs

ByPeter J. Dukes, Richard M. Wilson

chapter 8|28 pages

Number Theory and Finite Fields

ByJeffrey H. Dinitz, Hugh C. Williams

chapter 9|28 pages

Finite Groups and Designs

ByLeo G. Chouinard II, Robert Jajcay, Spyros S. Magliveras

chapter 10|5 pages

10Designs and Matroids

ByPeter J. Cameron, Michel M. Deza

chapter 11|16 pages

Strongly Regular Graphs

ByAndries E. Brouwer

chapter 12|7 pages

12Directed Strongly Regular Graphs

ByAndries E. Brouwer, Sylvia A. Hobart

chapter 13|8 pages


ByEdward Spence