Final answer:
The ideal conditions for increased metallic conductivity are having fewer valence electrons and a larger atomic radius, as these factors allow electrons to move more freely.
Step-by-step explanation:
The combination of factors most suitable for increasing the electrical conductivity of metals is fewer valence electrons and a larger atomic radius. This is because metals with fewer valence electrons can lose these electrons more easily, which contributes to conductivity. Furthermore, a larger atomic radius implies that these valence electrons are further away from the nucleus and therefore can be removed more easily, enhancing conductivity.