Combinatorial Testing
Combinatorial testing systematically tests combinations of input parameters — not every possible combination, which grows exponentially, but a mathematically chosen subset that still covers all pairs (or triples) of parameter values at least once. It's the general technique that pairwise testing is the most common specific case of.
Most real-world defects triggered by parameter combinations involve just two or three interacting values, not all of them at once — which is the empirical justification for combinatorial testing's core bet: covering all pairs or triples catches the large majority of combination-related bugs at a fraction of the cost of exhaustive testing.
Tools exist specifically to generate these reduced test sets (NIST's ACTS is a well-known free one) — feed in the parameters and their possible values, and the tool outputs the minimal set of test cases needed to guarantee full pairwise (or higher-order) coverage.
