```python
"""Firmware build selection within an installed release line."""


def compare_builds(a: str, b: str) -> int:
    left = [int(part) for part in a.split(".")]
    right = [int(part) for part in b.split(".")]
    for i in range(max(len(left), len(right))):
        x = left[i] if i < len(left) else 0
        y = right[i] if i < len(right) else 0
        if x > y:
            return 1
        if x < y:
            return -1
    return 0


def pick_upgrade(installed: str, offers: list) -> str | None:
    if not isinstance(installed, str) or not installed.isdigit() or "." in installed:
        raise ValueError("Installed build must be a valid dotted decimal number.")
    
    if not isinstance(offers, list):
        raise ValueError("Offers must be a list of strings.")
    
    best = None
    for offer in offers:
        if not isinstance(offer, str) or "." not in offer:
            continue
        
        parts = offer.split(".")
        if len(parts) < 2 or any(not part.isdigit() for part in parts):
            raise ValueError("Offer must be a valid dotted decimal number.")
        
        if parts[0] != installed.split(".")[0]:
            continue
        
        if compare_builds(offer, installed) > 0:
            best = offer
    
    return best
```