Sure! Here's a test case generator for the problem statement "Zero AND Subsets":

```python
import random

def tcgen():
    N = random.randint(1, 10**5)
    
    A = [random.randint(0, 2**20 - 1) for _ in range(N)]
    
    return N, A

# Example usage
if __name__ == "__main__":
    for _ in range(5):  # Generate 5 test cases
        N, A = tcgen()
        print(N)
        print(" ".join(map(str, A)))
```

This generator will create random test cases with the constraints specified:

1. The number of elements \(N\) is between 1 and \(10^5\).
2. Each element \(a_i\) in the multiset is a non-negative integer between 0 and \(2^{20} - 1\).

You can run this function to generate test cases for the problem "Zero AND Subsets". The output will be a randomly generated value for \(N\) and a list \(A\) of size \(N\) with elements in the specified range.