  After the correction of an inaccurate result in the reference, the author
uses five different methods, and gets five different inequalities on the
Hausdorff measure of the Cartesian product of the middle third Cantor set with
itself: $$H^s (C\times C)\leq 1.548563$$ $$H^s (C\times C)\leq 1.504975$$ $$H^s
(C\times C)\leq 1.502878$$ $$H^s (C\times C)\leq 1.503263$$ $$H^s (C\times
C)\leq 1.502483.$$ The main theory of this paper is the best among them, which
is $$H^s (C\times C)\leq 1.502483.$$
