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Nelsen et al.  find bounds for bivariate distribution functions when there are constraints on the values of its quartiles. Tankov  generalizes this work by giving explicit expressions for the best upper and lower bounds for a bivariate copula when its values on a compact subset of [0 1] 2 are known. He shows that they are quasi-copulas and not necessarily copulas. Tankov  and Bernard et al.  both give sufficient conditions for these bounds to be copulas. In this note we givedoi:10.2478/demo-2013-0002 fatcat:uq5ylkeaxngj5pizvb772ghgdy