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Making the Mols Table

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Computational and Constructive Design Theory

Abstract

This paper is not to be read by the faint of heart. No proofs are given, but it contains statements of a truly alarming number of constructions for transversal designs and incomplete transversal designs.

The paper is a record of an attempt to construct tables of the best results implied by known constructions for the existence of certain classes of mutually orthogonal latin squares and incomplete latin squares.

Sections §1–6 establish the mathematical background for the paper. We begin with basic definitions in §1. Then the following five sections state a fairly complete collection of construction techniques. It may well be impossible to write a complete list of variants of known constructions, and it is certainly beyond reason to do so. We content ourselves with a large battery of the constructions that have been exploited in the literature.

In §7–9, we describe a package developed in Maple which instantiates most (but not all) of the constructions in code. Issues in the design of this package are addressed, and a discussion of the architecture of the package is given.

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Author information

Authors and Affiliations

  1. Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, N2L3G1, Canada

    Jeffrey H. Dinitz

  2. Department of Mathematics and Statistics, University of Vermont, Burlington, Vermont, 05405, USA

    Charles J. Colbourn

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  1. Charles J. Colbourn
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  2. Jeffrey H. Dinitz
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Editors and Affiliations

  1. Department of Mathematics, Southern Illinois University, 62901-4408, Carbondale, Illinois, USA

    W. D. Wallis

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Colbourn, C.J., Dinitz, J.H. (1996). Making the Mols Table. In: Wallis, W.D. (eds) Computational and Constructive Design Theory. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-2497-4_5

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  • DOI: https://doi.org/10.1007/978-1-4757-2497-4_5

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