If your language lacks overt determiners for one or more of the categories, are those categories expressed at all? (Many languages lack definite/indefinite determiners, but can optionally express indefiniteness with numeral phrases. Other languages might have an overt definite determiner, but no over indefinite determiner.)
We're still not dealing with agreement, so our grammars will overgenerate (i.e., license sentences with agreement mismatches between determiners). Nonetheless, go ahead and collect the full paradigm for each determiner (e.g., French le, la, les) if your language marks gender or case or anything else on determiners. That way, you can at least parse good sentences.