def _create_file_name_from_complex_index(complex_):
    """Create a file name from a complex index."""
    choice = "".join([str(int(x)) for x in complex_[1]])
    if len(complex_) == 3:
        file_name = f"{complex_[0]}_{choice}_{complex_[2]}.parquet"
    elif len(complex_) == 2:
        file_name = f"{complex_[0]}_{choice}.parquet"
    else:
        raise NotImplementedError

    return file_name