```python
from typing import List

def hex_groups(values: List[int], width: int) -> str:
    if not isinstance(values, list):
        raise ValueError("values must be a list")
    
    for value in values:
        if not isinstance(value, int) or value < 0 or value > 255:
            raise ValueError("each byte must be an integer between 0 and 255")
    
    if not isinstance(width, int) or width <= 0:
        raise ValueError("width must be a positive integer")
    
    hex_values = [f"{value:02x}" for value in values]
    groups = [hex_values[i:i+width] for i in range(0, len(hex_values), width)]
    return " ".join(" ".join(group) for group in groups)
```