Jeffrey H. Dinitz

CRC Handbook of Combinatorial Designs

Balanced Incomplete Block Designs and t-Designs2-(v,k,l) Designs of Small OrderBIBDs with Small Block Sizet-Designs, t = 3Steiner SystemsSymmetric DesignsResolvable and Near Resolvable DesignsLatin Squares, MOLS, and Orthogonal ArraysLatin SquaresMutually Orthogonal Latin Squares (MOLS)Incomplete MOLSOrthogonal Arrays of Index More Than OneOrthogonal Arrays of Strength More Than TwoPairwise Balanced DesignsPBDs and GDDs: The BasicsPBDs: Recursive ConstructionsPBD-ClosurePairwise Balanced Designs as Linear SpacesPBDs and GDDs of Higher IndexPBDs, Frames, and ResolvabilityOther Combinatorial DesignsAssociation SchemesBalanced (Part) Ternary DesignsBalanced Tournament DesignsBhaskar Rao DesignsComplete Mappings and Sequencings of Finite GroupsConfigurationsCostas ArraysCoveringsCycle SystemsDifference FamiliesDifference MatricesDifference Sets: AbelianDifference Sets: NonabelianDifference Triangle SetsDirected DesignsD-Optimal MatricesEmbedding Partial QuasigroupsEquidistant Permutation ArraysFactorial DesignsFrequency SquaresGeneralized QuadranglesGraph Decompositions and DesignsGraphical DesignsHadamard Matrices and DesignsHall Triple SystemsHowell DesignsMaximal Sets of MOLSMendelsohn DesignsThe Oberwolfach ProblemOrdered Designs and Perpendicular ArraysOrthogonal DesignsOrthogonal Main Effect PlansPackingsPartial GeometriesPartially Balanced Incomplete Block DesignsQuasigroupsQuasi-Symmetric Designs(r,l)-DesignsRoom SquaresSelf-Orthogonal Latin Squares (SOLS)SOLS with a Symmetric Orthogonal Mate (SOLSSOM)Sequences with Zero AutocorrelationSkolem SequencesSpherical t-DesignsStartersTrades and Defining Sets(t,m,s)-NetsTuscan Squarest-Wise Balanced DesignsUniformly Resolvable DesignsVector Space DesignsWeighing Matrices and Conference MatricesWhist TournamentsYouden Designs, GeneralizedYouden SquaresApplicationsCodesComputer Science: Selected ApplicationsApplications of Designs to CryptographyDerandomizationOptimality and Efficiency: Comparing Block DesignsGroup TestingScheduling a TournamentWinning the LotteryRelated Mathematics and Computational MethodsFinite Groups and DesignsNumber Theory and Finite FieldsGraphs and MultigraphsFactorizations of GraphsStrongly Regular GraphsTwo-GraphsClassical GeometriesProjective Planes, NondesarguesianComputational Methods in Design TheoryIndex

Handbook of Combinatorial Designs, Second Edition

PREFACE INTRODUCTION NEW! Opening the Door NEW! Design Theory: Antiquity to 1950 BLOCK DESIGNS 2-(v, k, ?) Designs of Small Order NEW! Triple Systems BIBDs with Small Block Size t-Designs with t = 3 Steiner Systems Symmetric Designs Resolvable and Near-Resolvable Designs LATIN SQUARES Latin Squares Quasigroups Mutually Orthogonal Latin Squares (MOLS) Incomplete MOLS Self-Orthogonal Latin Squares (SOLS) Orthogonal Arrays of Index More Than One Orthogonal Arrays of Strength More Than Two PAIRWISE BALANCED DESIGNS PBDs and GDDs: The Basics PBDs: Recursive Constructions PBD-Closure NEW! Group Divisible Designs PBDs, Frames, and Resolvability Pairwise Balanced Designs as Linear Spaces HADAMARD MATRICES AND RELATED DESIGNS Hadamard Matrices and Hadamard Designs Orthogonal Designs D-Optimal Matrices Bhaskar Rao Designs Generalized Hadamard Matrices Balanced Generalized Weighing Matrices and Conference Matrices Sequence Correlation Complementary, Base and Turyn Sequences NEW! Optical Orthogonal Codes OTHER COMBINATORIAL DESIGNS Association Schemes Balanced Ternary Designs Balanced Tournament Designs NEW! Bent Functions NEW! Block-Transitive Designs Complete Mappings and Sequencings of Finite Groups Configurations Correlation-Immune and Resilient Functions Costas Arrays NEW! Covering Arrays Coverings Cycle Decompositions Defining Sets NEW! Deletion-Correcting Codes Derandomization Difference Families Difference Matrices Difference Sets Difference Triangle Sets Directed Designs Factorial Designs Frequency Squares and Hypercubes Generalized Quadrangles Graph Decompositions NEW! Graph Embeddings and Designs Graphical Designs NEW! Grooming Hall Triple Systems Howell Designs NEW! Infinite Designs Linear Spaces: Geometric Aspects Lotto Designs NEW! Low Density Parity Check Codes NEW! Magic Squares Mendelsohn Designs NEW! Nested Designs Optimality and Efficiency: Comparing Block Designs Ordered Designs, Perpendicular Arrays and Permutation Sets Orthogonal Main Effect Plans Packings Partial Geometries Partially Balanced Incomplete Block Designs NEW! Perfect Hash Families NEW! Permutation Codes and Arrays NEW! Permutation Polynomials NEW! Pooling Designs NEW! Quasi-3 Designs Quasi-Symmetric Designs (r, ?)-designs Room Squares Scheduling a Tournament Secrecy and Authentication Codes Skolem and Langford Sequences Spherical Designs Starters Superimposed Codes and Combinatorial Group Testing NEW! Supersimple Designs Threshold and Ramp Schemes (t,m,s)-Nets Trades NEW! Turan Systems Tuscan Squares t-Wise Balanced Designs Whist Tournaments Youden Squares and Generalized Youden Designs RELATED MATHEMATICS Codes Finite Geometry NEW! Divisible Semiplanes Graphs and Multigraphs Factorizations of Graphs Computational Methods in Design Theory NEW! Linear Algebra and Designs Number Theory and Finite Fields Finite Groups and Designs NEW! Designs and Matroids Strongly Regular Graphs NEW! Directed Strongly Regular Graphs Two-Graphs BIBLIOGRAPHY INDEX

Some new row-complete Latin squares

Abstract Row-complete Latin squares of orders 9, 15, 21 and 27 are given. The square of order 9 is the smallest possible odd order row-complete Latin square.