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What is both the most efficient way to reach the cap of 85% physical damage reduction (567 Armor)?

Can it be reached without smithing/enchanting perks? Is it more efficient to not get some smithing or enchanting perks and just get heavy armor perks? Or is there some combination of crafting and heavy armor perks that gets to 567 armor with a smaller investment of perk points?

For purposes of this question, most efficient is defined as the smallest possible amount of perks used to acquire the stated physical damage reduction, passively - i.e. without popping pots (temporary) or using extra buffs from stones, blessings, or +Heavy Armor skill enchants (to keep those slots on equipment free for other enhancements).

What is both the most efficient way to reach the cap of 85% physical damage reduction (567 Armor)?

Can it be reached without smithing/enchanting perks? Is it more efficient to not get some smithing or enchanting perks and just get heavy armor perks? Or is there some combination of crafting and heavy armor perks that gets to 567 armor with a smaller investment of perk points?

For purposes of this question, most efficient is defined as the smallest possible amount of perks used to acquire the stated physical damage reduction, passively - i.e. without popping pots (temporary) or using extra buffs from stones, blessings, or +Heavy Armor skill enchants (to keep those slots on equipment free for other enhancements). Also, any skill used to achieve this can be assumed to be leveled to 100 (for example Heavy Armor could be assumed to be already leveled to 100).

Since the cap is more of a "soft" cap than a hard cap (from what I read it seems anyways)... what is both the most efficient way to reach 80% physical damage reduction as well as 85% physical damage reduction? Can you reach either without smithing/enchanting perks? Is it more efficient to not get some smithing or enchanting perks and just get heavy armor perks? Can you do it with a combination of less smithing/alchemy/enchanting/heavy armor perks than it can with other combination? Most efficient being... least amount of perks used to acquire the stated physical damage reduction and with it being passive without popping pots (temporary) or using extra buffs from sign/blessings. Edit: Also, no using heavy armor skill enchants as they would be used for other things.

What is both the most efficient way to reach the cap of 85% physical damage reduction (567 Armor)?

Can it be reached without smithing/enchanting perks? Is it more efficient to not get some smithing or enchanting perks and just get heavy armor perks? Or is there some combination of crafting and heavy armor perks that gets to 567 armor with a smaller investment of perk points?

For purposes of this question, most efficient is defined as the smallest possible amount of perks used to acquire the stated physical damage reduction, passively - i.e. without popping pots (temporary) or using extra buffs from stones, blessings, or +Heavy Armor skill enchants (to keep those slots on equipment free for other enhancements).