The antilogarithm searches a string for matches to a key, once it matches a character of the string to the first character of the key, it begins comparing the next character of the string, and if that matches, then it compares the next, and so on until it fails.
So the way to maximize comparisons is to not only have the algorithm fail _just_ before finding a match, but to also hide partial matches within such a string so that it has to also consider that partial match after it fails.
For example, given the key "ABABCDB" we could use the following: $$ABABABAB$$
Here it will compare the first four characters $ABAB$, then it will go back and start at the second $A$ and compare $ABAB$ again, then the third, and so on. It will compare fail on each turn after $$ABAB \\\ ABAB \\\ ABAB \\\AB$$
So in this case, we have $14$ comparisons.
Hope that helps.