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Journal of Inforamtion Science and Engineering, Vol.13 No.4, pp.605-613 (December 1997)
Constructing N£^ Latin Squares for£^°ŕ2£\

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£^ latin square of order n is an n°—n latin square containing no latin subsquare of order£^ for 1 <£^ < n. It has been shown in the literature that if n°ŕ2p3q there exists an n°—n latin square without latin subsquare of order£^ for£^< n. In this paper, combining with the known results, we show that for any integer n there is an n°—n N£^ latin square if£^ is not a power of two .

Keywords: latin square, subsquare free, constructive proof

Received December 4, 1995; revised October 30, 1996.
Communicated by Wen-Lien Hsu.