Depends if you can return to the departure airfield having taken into account the meteorological and/or performance considerations.
If an aircraft can commence an approach to the airfield in Cat 3A conditions after the loss of an engine then in theory that would preclude the absolute need for a take off alternate to be specified. If not, then one must be nominated and it would need to be above the applicable landing minima taking the same performance considerations into account, as well as the other applicable terrain and distance requirements. Obviously that wouldn't be the wisest course of action, but that is the requirement.