Designs 2002: Further Computational and Constructive Design Theory PDF
Preview Designs 2002: Further Computational and Constructive Design Theory
DESIGNS 2002 Mathematics and Its Applications Managing Editor: M. Hazewinkel Centre for Mathematics and Computer Science, Amsterdam, The Netherlands Volume 563 DESIGNS 2002 Further Computational and Constructive Design Theory Edited by W. D. WALLIS Southern Illinois University .... " Kluwer Academic Publishers Boston/Dordrecht/London Distritutors for North, Central and South America: Kluwer Academic Publishers 101 Philip Drive Assinippi Park Norwell, Massachusetts 02061 USA Telephone (781) 871-6600 Fax (781) 871-6528 E-Mail <[email protected]> Distributors for all other countries: Kluwer Academic Publishers Group Post Office Box 322 3300 AH Dordrecht, THE NETHERLANDS Telephone 31786576000 Fax 31 78 6576 474 E-Mail <[email protected]> ~t Electronic Services <http://www.wkap.nl> Library of Congress Cataloging-in-Publication Wallis, Waiter D. Designs 2002: Further Computational and Constructive Design Theory ISBN-13:978-1-4613-7958-4 e-ISBN-13:978-1-4613-0245-2 DOl: 10.1007/978-1-4613-0245-2 Copyright 0 2003 by Kluwer Academic Publishers All rights reserved. No part ofthis pUblication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photo-copying, microfilming, recording, or otherwise, without the prior written permission of the publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Permissions for books published in the USA: perm; 55; ODS@wkap com Permissions for books published in Europe: [email protected] Printed on acid-free paper. Contents Preface xi 1 1 The Existence of 2-S0LSSOMs R. Julian R. Abel and F. E. Bennett 1 Introduction 1 2 Direct Constructions 4 3 Recursive Constructions 8 2 23 Conjugate Orthogonal Diagonal Latin Squares with Missing Subsquares Frank E. Bennett, Beiliang Du and Hantao Zhang 1 Introduction 24 2 Preliminaries 27 3 Direct Construction 30 4 Recursive Construction 33 5 A General Bound 37 6 The Case 2 :S n :S 6 41 vi DESIGNS 2002 3 47 Combinatorial Trades: a Survey of Recent Results Elizabeth J. Billington 1 Introduction and Preliminaries 47 2 Trades in designs 48 3 Trades in latin squares 53 4 Trade uses 54 5 Latin representations and trades used in tripartite decomposi- tions 56 6 f-L-way trades 58 7 Graphical trades 60 8 Future directions 62 4 69 Two-stage Generalized Simulated Annealing for the Construction of Change-Over Designs Yuk W. Cheng, Deborah J. Street, William H. Wilson 1 Introduction 69 2 Notation and Definitions 71 3 A Two Stage Generalized Simulated Annealing Algorithm 73 4 Performance of the Two-Stage GSA 75 5 81 New Lower Bounds on the Maximum Number of Mutually Orthog onal Steiner Triple Systems J. H. Din'itz and P. Dukes 1 Introduction 81 2 Starters over Finite Fields 83 3 Automorphisms and Hill-climbing 92 4 Conclusion 99 Contents vii 6 103 On minimal defining sets in AG(d, 3) Diane Donovan, Abdallah Khodkar and Anne Penfold Street 1 Background 104 2 Introduction 105 3 Further Preliminaries 116 4 Proof of the Main Theorem 121 5 Sets of good hyperplanes in AG(d, 3) 124 6 Related critical sets 127 7 Appendix 129 7 133 Hadamard Matrices, Orthogonal designs and Construction Algorithms Stelios Georgiou, Christos Koukouvinos and Jennifer Seberry 1 Algorithms for constructing Hadamard matrices 134 2 On inequivalent Hadamard matrices 163 3 Algorithms for constructing orthogonal designs 176 4 Short amicable sets and Kharaghani type orthogonal designs 193 8 207 Constructing a Class of Designs with Proportional Balance Ken Gray and Anne Penfold Street 1 Proportionally balanced designs 208 2 The method of construction 211 3 Feasible parameters for Q = 2, 3 and 4 214 4 Constructions motivated by Construction 5 218 viii DESIGNS 2002 9 227 Constructions Using Balanced n-ary Designs Malcolm Greig 1 Introduction 227 2 Balanced n-ary Designs 229 3 Our Construction 230 4 Some Examples 232 5 Some Non-existence Results 235 6 An Improved Construction 238 7 Quadratic Residues 240 8 Another Improvement 243 9 An Application 246 10 More Difference Families 247 10 255 Sets of Steiner 'friple Systems of Order 9 Revisited T. S. Griggs and A. Rosa 1 Introd uction 255 2 Large sets 257 3 Results 260 4 Uniformly intersecting sets 263 11 277 Solving Isomorphism Problems for t-Designs Reinhard Laue 1 Introduction 277 2 Basics 279 3 Moebius Inversions 282 4 Extensions of designs 293 Contents ix 12 301 Finding Double Youden Rectangles N. C. K. Phillips and D. A. Preece 1 Introduction 301 2 Definitions and Literature 302 3 Examples 302 4 Searching for a 13-cyclic 13 X 40 DYR 306 5 Isomorphism 309 6 Further Properties of our new DYRs 313 7 Check for Balance 314 13 317 Kirkman Triple Systems and their Generalizations: A Survey Rolf S. Rees, W. D. Wallis 1 Introduction 318 2 Constructions for Kirkman Trirle Systems and Nearly Kirk- man Triple Systems for all admIssible orders 334 3 Early Generalizations 342 4 Resolvable Packings and Coverings of v points where v =t 0 (mod 3) 348 5 Other Generalizations 359 6 Conclusion and Acknowledgements 363
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