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The use of hill‐climbing to construct orthogonal steiner triple systems
Author(s) -
Gibbons Peter B.,
Mathon Rudolf
Publication year - 1993
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.3180010105
Subject(s) - mathematics , combinatorics , construct (python library) , steiner system , orthogonal array , climbing , set (abstract data type) , discrete mathematics , computer science , statistics , programming language , history , archaeology , taguchi methods
In a related article, Colbourn, Gibbons, Mathon, Mullin, and Rosa [7] have shown that a pair of orthogonal Steiner triple systems exists for all v ≡ 1, 3 (mod 6), v ≥ 7 and v ≠ 9. This result is based on the construction of a finite set of pairs of orthogonal Steiner triple systems followed by the application of recursive constructions to settle the remaining undecided cases. In this article we report on the computational aspects of that investigation, and in particular the remarkable success of the hill‐climbing method. © 1993 John Wiley & Sons, Inc.