What's the standard way of implementing an automaton with not-transitions?

What's the standard way of implementing an automaton with not-transitions?

The naive implementation of a FA would have the node look like:
struct Node {
string label;
Node*[char] trans;
}
But what if one of your transitions is "![a]" (anything but the char 'a').
And your alphabet is too huge to store all possible chars that are not
'a'. Do you see what I mean?