Designs 2002 [Elektronische Ressource] : Further Computational and Constructive Design Theory | Wallis, W. D

Designs 2002: Further Computational and Constructive Design Theory
Author: W. D. Wallis
Published by Springer US
ISBN: 978-1-4613-7958-4
DOI: 10.1007/978-1-4613-0245-2

Table of Contents:

• The Existence of 2-SOLSSOMs
• Conjugate Orthogonal Diagonal Latin Squares with Missing Subsquares
• Combinatorial Trades: A Survey of Recent Results
• Two-Stage Generalized Simulated Annealing for the Construction of Change-Over Designs
• New Lower Bounds on the Maximum Number of Mutually Orthogonal Steiner Triple Systems
• On Minimal Defining Sets in AG(d,3)
• Hadamard Matrices, Orthogonal Designs and Construction Algorithms
• Constructing a Class of Designs with Proportional Balance
• Constructions Using Balanced n-ary Designs
• Sets of Steiner Triple Systems of Order 9 Revisited
• Solving Isomorphism Problems for t-Designs
• Finding Double Youden Rectangles
• Kirkman Triple Systems and Their Generalizations: A Survey

This volume is a sequel to our 1996 compilation, Computational and Constructive Design Theory. Again we concentrate on two closely re lated aspects of the study of combinatorial designs: design construction and computer-aided study of designs. There are at least three classes of constructive problems in design theory. The first type of problem is the construction of a specific design. This might arise because that one particular case is an exception to a general rule, the last remaining case of a problem, or the smallest unknown case. A good example is the proof that there is no projective plane of parameter 10. In that case the computations involved were not different in kind from those which have been done by human brains without electronic assistance; they were merely longer. Computers have also been useful in the study of combinatorial spec trum problems: if a class of design has certain parameters, what is the set of values that the parameters can realize? In many cases, there is a recursive construction, so that the existence of a small number of "starter" designs leads to the construction of infinite classes of designs, and computers have proven very useful in finding "starter" designs