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Journal of Information Science and Engineering, Vol. 13 No. 4, pp. 605-613

Constructing N_γ Latin Squares forγ≠2^α

Shian-Shyong Tseng, Bertrand M. T. Lin^* and Sue Huei Liu^#
Department of Computer and Information Science
National Chiao-Tung University
Hsinchu, Taiwan 300, R.O.C.
^* Department of Information Management
Ming-Chuan University
Taipei 111, R.O.C.
^# Department of Computer Science and Information Engineering
National Chiao-Tung University
Hsinchu, Taiwan 300, R.O.C.

An N_γ latin square of order n is an n×n latin square containing no latin subsquare of orderγ for 1 <γ < n. It has been shown in the literature that ifn≠2^p3^q there exists an n×n latin square without latin subsquare of orderγ forγ< n. In this paper, combining with the known results, we show that for any integer n there is an n×n N_γlatin square ifγ is not a power of two .

Keywords: latin square, subsquare free, constructive proof

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