The existence of Latin squares without orthogonal mates

DOI10.1007/s10623-006-8168-9zbMath1180.05023OpenAlexW1988115705MaRDI QIDQ851741

Bridget S. Webb, Ian M. Wanless

Publication date: 22 November 2006

Published in: Designs, Codes and Cryptography (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10623-006-8168-9

zbMATH Keywords

Latin squareMOLSLatin tradeBachelor squareTransversal

Mathematics Subject Classification ID

Orthogonal arrays, Latin squares, Room squares (05B15)

Related Items (26)

Completing partial transversals of Cayley tables of Abelian groups ⋮ Latin squares with restricted transversals ⋮ Latin Squares with Restricted Transversals ⋮ Balanced diagonals in frequency squares ⋮ Cycle structure of autotopisms of quasigroups and latin squares ⋮ Latin squares without orthogonal mates ⋮ On the existence of unparalleled even cycle systems ⋮ Embedding partial Latin squares in Latin squares with many mutually orthogonal mates ⋮ Covers and partial transversals of Latin squares ⋮ Permanents of multidimensional matrices: Properties and applications ⋮ Remoteness of permutation codes ⋮ Monogamous latin squares ⋮ Almost all Steiner triple systems are almost resolvable ⋮ The chromatic number of finite group Cayley tables ⋮ The theory and application of latin bitrades: A survey ⋮ Enumerating extensions of mutually orthogonal Latin squares ⋮ Indivisible partitions of Latin squares ⋮ Enumeration of MOLS of small order ⋮ Transversals of Latin squares and covering radius of sets of permutations ⋮ Latin squares with no small odd plexes ⋮ Unnamed Item ⋮ Bachelor latin squares with large indivisible plexes ⋮ Orthogonality of approximate Latin squares and quasigroups ⋮ A gap for the maximum number of mutually unbiased bases ⋮ Latin trades in groups defined on planar triangulations ⋮ Mutually orthogonal binary frequency squares

Cites Work

• Latin squares without orthogonal mates
• Maximal sets of mutually orthogonal Latin squares
• Small latin squares, quasigroups, and loops
• On orthogonal Latin squares

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