Generating many random numbers within a range with some exceptions in java

I need to generate lots of random numbers within a range with some exceptions. Right now I'm planning to do it in this way,

public class Main
{
    static List<Integer> except = Arrays.asList(5, 6, 11, 12, 17, 18, 23, 25, 28, 29);
    
    
    public static void main(String[] args) {
        
        List<Integer> randomNums = new ArrayList<>();
        
        Random random = new Random();
        
        int z;
        for(i=0; i<20; i++) {
            z = random.nextInt(30);
            while(except.contains(z)) z = random.nextInt(30);

            randomNums.add(z);
        }           
        
        System.out.println(randomNums);
    }
}

In my case the size of "except" and "randomNums" will be much higher. So the code will spend much time in the while to avoid numbers that I don't want.

I'm curious to know can I speed up my code? If I can remove the while loop then definitely it will be an O(n). But how can I do that. Thanks.