minimum
The smallest amount or number that is allowed or possible.
Minimum means the smallest amount, number, or degree possible or allowed. When a store sets a minimum purchase of ten dollars for credit card payments, you can't use your card unless you're buying at least that much. When a recipe calls for a minimum of two cups of flour, you need at least two cups, though you could use more.
Think of a thermometer showing the minimum temperature for the day: that's the coldest it got, the lowest point the mercury reached. A swimming pool might have a minimum depth of three feet at the shallow end.
Teachers often set minimum requirements for assignments: a book report might need a minimum of three pages, meaning three pages is acceptable but four or five would be fine too. The opposite of minimum is maximum, which means the most or largest amount allowed.
When someone does the bare minimum, they're doing exactly the least amount required and nothing more. A student who completes the minimum homework but never reads ahead or asks questions is meeting the basic requirement without going further. When you exceed the minimum, you're going beyond what's merely required.