Cavenagh, Nicholas J.Ramadurai, Reshma2017-05-222016-08-042017-05-222017Cavenagh, N., & Ramadurai, R. (2017). On the Distances between Latin Squares and the Smallest Defining Set Size. Journal of Combinatorial Designs, 25(4), 147–158. https://doi.org/10.1002/jcd.215291063-8539https://hdl.handle.net/10289/11068In this note, we show that for each Latin square L of order n≥2 , there exists a Latin square L’≠L of order n such that L and L’ differ in at most 8√n cells. Equivalently, each Latin square of order n contains a Latin trade of size at most 8√n. We also show that the size of the smallest defining set in a Latin square is Ω(n³/²).application/pdfenThis is an author’s accepted version of an article published in the journal: Journal of combinatorial designs. © 2017 Wiley.Science & TechnologyPhysical SciencesMathematicsLatin squareLatin tradedefining setcritical setHamming distanceLatin squareLatin tradedefining setHamming distanceJournal Article10.1002/jcd.215291520-6610