Maximum number of clues in a Sudoku game that does not produce a unique solution

I conclude that the largest number of starting clues for any Sudoku to be ambiguous is 77 (81 - 4), and you can construct it by finding a 'rectangle' with ones on two opposite corners and twos on the other two opposite corners. Remove all four of them. Now you can solve it in two ways: it is ambiguous.

A random Sudoku from the Internet:

77.

Label as a matrix, rows 1 down to 9, columns 1 through 9. Begin with any completely filled in grid such that $$a_{11} = 1,a_{12} = 2,a_{41} = 2,a_{42} = 1. $$ The important thing is that the first pair are in the upper left 3 by 3 box, while the other pair are in the middle left 3 by 3 box.

Now, delete those four entries.