[stick]

Making a test with 0% false negative rate is a piece of cake:

if (test_taken == true) { test_result = true; }

No negatives means no false negatives. ;)

But seriously, this is the classic trade-off between high sensitivity (no false negatives) and high specificity (essentially no false positives). Usually, the lower you set your threshold for detection the more likely you are to tell some people they have the disease when they actually don't. Where you set that bar depends on what you're trying to accomplish and forces you consider the harms associated with telling people they have disease when they don't or missing disease in someone who does.