Further results on mutually nearly orthogonal Latin squares

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• 作者：Ke-jun Chen ; Yong Zhang ; Guang-zhou Chen…
• 关键词：Latin square ; orthogonal ; nearly orthogonal ; holey
• 刊名：Acta Mathematicae Applicatae Sinica, English Series
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：32
• 期：1
• 页码：209-220
• 全文大小：242 KB
• 参考文献：[1]Abel, R.J.R., Bennett, F.E., Ge. G. The existence of four HMOLS with equal sized holes. Des. Codes. Cryptogr., 26: 7–31 (2002)MathSciNet CrossRef MATH
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  [5]Dénes, J., Keedwell, A.D. Latin squares and their applications. Academic Press, New York, London, 1974MATH
  [6]Dinitz, J.H., Stinson, D.R. MOLS with holes. Discrete Math., 44: 145–154 (1983)MathSciNet CrossRef MATH
  [7]Ge, G., Abel, R.J.R. Some new HSOLSSOMs of type hn and 1nu1. J. Combin. Designs, 9: 435–444 (2001)MathSciNet CrossRef MATH
  [8]Li, P.C., Van Rees, G.H.J. Nearly orthogonal Latin squares. J. Combin. Math. Combin. Comput., 62: 13–24 (2007)MathSciNet MATH
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• 作者单位：Ke-jun Chen (1)
  Yong Zhang (2)
  Guang-zhou Chen (3)
  Wen Li (2)
  
  1. Department of Mathematics, Taizhou University, Taizhou, 225300, China
  2. Department of Mathematics, Yancheng Teachers University, Yancheng, 224002, China
  3. College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, 050024, China
  
• 刊物主题：Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics;
• 出版者：Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
• ISSN：1618-3932

文摘

Nearly orthogonal Latin squares are useful for conducting experiments eliminating heterogeneity in two directions and using different interventions each at each level. In this paper, some constructions of mutually nearly orthogonal Latin squares are provided. It is proved that there exist 3 MNOLS(2m) if and only if m ≥ 3 and there exist 4 MNOLS(2m) if and only if m ≥ 4 with some possible exceptions.