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On the maximality of a set of mutually orthogonal Sudoku Latin Squares

Jozefien D'haeseleer (UGent) , Klaus Metsch (UGent) , Leo Storme (UGent) and Geertrui Van de Voorde (UGent)
(2017) DESIGNS CODES AND CRYPTOGRAPHY. 84(1-2). p.143-152
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Abstract
The maximum number of mutually orthogonal Sudoku Latin squares (MOSLS) of order is n = m(2) is n - m. In this paper, we construct for n = q(2), q a prime power, a set of q(2) - q - 1 MOSLS of order q(2) that cannot be extended to a set of q(2) - q MOSLS. This contrasts to the theory of ordinary Latin squares of order n, where each set of n - 2 mutually orthogonal Latin Squares (MOLS) can be extended to a set of n - 1 MOLS (which is best possible). For this proof, we construct a particular maximal partial spread of size q(2) - q + 1 in PG(3,q) and use a connection between Sudoku Latin squares and projective geometry, established by Bailey, Cameron and Connelly.
Keywords
Latin square, MOLS, Sudoku, MOSLS, Maximal partial spread, Regular spread

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Chicago
D’haeseleer, Jozefien, Klaus Metsch, Leo Storme, and Geertrui Van de Voorde. 2017. “On the Maximality of a Set of Mutually Orthogonal Sudoku Latin Squares.” Designs Codes and Cryptography 84 (1-2): 143–152.
APA
D’haeseleer, J., Metsch, K., Storme, L., & Van de Voorde, G. (2017). On the maximality of a set of mutually orthogonal Sudoku Latin Squares. DESIGNS CODES AND CRYPTOGRAPHY, 84(1-2), 143–152.
Vancouver
1.
D’haeseleer J, Metsch K, Storme L, Van de Voorde G. On the maximality of a set of mutually orthogonal Sudoku Latin Squares. DESIGNS CODES AND CRYPTOGRAPHY. 2017;84(1-2):143–52.
MLA
D’haeseleer, Jozefien et al. “On the Maximality of a Set of Mutually Orthogonal Sudoku Latin Squares.” DESIGNS CODES AND CRYPTOGRAPHY 84.1-2 (2017): 143–152. Print.
@article{8525327,
  abstract     = {The maximum number of mutually orthogonal Sudoku Latin squares (MOSLS) of order is n = m(2) is n - m. In this paper, we construct for n = q(2), q a prime power, a set of q(2) - q - 1 MOSLS of order q(2) that cannot be extended to a set of q(2) - q MOSLS. This contrasts to the theory of ordinary Latin squares of order n, where each set of n - 2 mutually orthogonal Latin Squares (MOLS) can be extended to a set of n - 1 MOLS (which is best possible). For this proof, we construct a particular maximal partial spread of size q(2) - q + 1 in PG(3,q) and use a connection between Sudoku Latin squares and projective geometry, established by Bailey, Cameron and Connelly.},
  author       = {D'haeseleer, Jozefien and Metsch, Klaus and Storme, Leo and Van de Voorde, Geertrui},
  issn         = {0925-1022},
  journal      = {DESIGNS CODES AND CRYPTOGRAPHY},
  keywords     = {Latin square,MOLS,Sudoku,MOSLS,Maximal partial spread,Regular spread},
  language     = {eng},
  number       = {1-2},
  pages        = {143--152},
  title        = {On the maximality of a set of mutually orthogonal Sudoku Latin Squares},
  url          = {http://dx.doi.org/10.1007/s10623-016-0234-3},
  volume       = {84},
  year         = {2017},
}

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