This link might help: http://en.wikipedia.org/wiki/Dutch_grammar#Adjectives_used_as_adverbs and scroll down to "Comparative and superlative" . Apparently when an adjective is used as an adverb, the superlative is always preceded by the neuter article "het". Note too what it says about using "de" instead of "het" in this situation.
Thanks v much......and for the link! Mostly v clear, but I don't get the bit about the superlative ever being an adverb (which I take to mean describing a verb, as in deze jas is het duurst(e)..... And even their example says inflective or non-inflective can both be used!