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Some new Orthogonal diagonal latin squares

Part of: Designs and configurations

Published online by Cambridge University Press:  09 April 2009

W. D. Wallis  and
L. Zhu
W. D. Wallis
Affiliation:
Department of Mathematics The University of NewcastleNewcastle, N.S.W. 2308, Australia
L. Zhu
Affiliation:
Department of Mathematics Kiangsu Teachers' CollegeSoochow, China
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Abstract

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A recursive construction for orthogonal diagonal latin squares, using group divisible designs, is presented. In consequence the numbers of orders for which the existence of such squares is in question is reduced to 72.

MSC classification

Secondary: 05B15: Orthogonal arrays, Latin squares, Room squares
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 34 , Issue 1 , February 1983 , pp. 49 - 54
Copyright
Copyright © Australian Mathematical Society 1983

References

[1]Denes, J. and Keedwell, A. D., Latin squares and their applications (Academic Press, New York, 1974).Google Scholar
[2]Hanani, H., ‘Balanced incomplete block designs and related designs’, Discrete Math. 11 (1975), 255–369.CrossRefGoogle Scholar
[3]Wallis, W. D. and Zhu, L., ‘Existence of orthogonal diagonal latin squares’, Ars Combinatoria 12 (1981), 51–68.Google Scholar
[4]Wang, S. M. P. and Wilson, R. M., ‘A few more squares, II’, Congressus Numerantium 21 (= Proceedings of the Ninth Southeastern Conference on Combinatorics. Graph Theory and Computing), 688.Google Scholar