Another way to do it is bitwise. I'm not familiar with the built-in php functions for this, but basically your first checkbox would be given a value of 1, the second 2, the third 4, the fourth 8, etc. You add them together where that position is yes (or 1). So first yes, second no, and third yes would be 5 (101 in base 2).
Storing 25 bits would require a number up to (226)-1, or 67,108,864.