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A few more balanced Room squares

Part of: Designs and configurations

Published online by Cambridge University Press:  09 April 2009

D. R. Stinson  and
S. A. Vanstone
D. R. Stinson
Affiliation:
Department of Computer, Science, University of Manibota, Winnipeg, Manitoba R3T 2N2, Canada
S. A. Vanstone
Affiliation:
Department of Combinatorics, and Optimization, St. Jerome's College, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
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Abstract

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The existence problem for balanced Room squares is, in general, unsolved. Recently, B. A. Anderson gave a construction for a class of these designs with side 2n − 1, where n is odd and n ≥ 3. For n even, the existence has not yet been settled. In this paper, we use the affine geometry of dimension 2 k and order 2, and a hill-climbing algorithm, to construct a number of new balanced Room squares directly. Recursive techniques based on finite geometries then give new squares of side 22k − 1 for infinitely many values of k.

MSC classification

Secondary: 05B25: Finite geometries

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 39 , Issue 3 , December 1985 , pp. 344 - 352
Copyright
Copyright © Australian Mathematical Society 1985

References

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