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Journal of Combinatorial Mathematics and Combinatorial Computing

  • Research article

Critical Sets for a Pair of Mutually Orthogonal Cyclic Latin Squares of Odd Order Greater than \( 9 \)

Rita SahaRay1, Avishek Adhikari2, Jennifer Seberry3
1Stat-Math Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata-700 108, India.
2 Applied Statistics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata-700 108, India.
3 Center for Computer Security Research, SITACS, University of Wollongong, NSW 2522, Australia
  • Published: 30/11/2005

Abstract

To date, investigations on critical sets for a set of mutually orthogonal Latin squares (MOLS) have been carried out only for small orders \( \leq 9 \). In this paper, we deal with a pair of cyclic orthogonal Latin squares of order \( n \), \( n \geq 11 \), \( n \) odd. Through the construction of a uniquely completable set, we give an upper bound on the size of the minimal critical set. In particular, for \( n = 15 \), a critical set achieving this bound is obtained.

Keywords: Back-circulant latin squares, Isotopic latin squares, Mutually orthogonal latin squares, Orthogonal arrays, Critical sets.
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Citation
Rita SahaRay, Avishek Adhikari, Jennifer Seberry. Critical Sets for a Pair of Mutually Orthogonal Cyclic Latin Squares of Odd Order Greater than \( 9 \)[J], Journal of Combinatorial Mathematics and Combinatorial Computing, Volume 055. 171-185. .