Construction jobs are a type of runner mission that can by accepted from any CityCom or Resistance Network terminal requiring you to construct an item from blueprints and construction parts provided by a designated representative of the faction the mission is for, and then hand those blueprints into another designated faction representative - usually a Faction Supply Manager. Construction jobs are available in 10 tech level increments starting at TL10 and ending at TL150 spread across the various difficulty categories available when selecting runner missions. Construction jobs higher than TL20 will use construction grease like normal construction tasks.
Required faction sympathies
Construction jobs require a certain amount of action sympathy with the faction offering the job for you to be able to accept the job. The lowest tech level missions - TL10 - require 6 faction sympathy. Each tech level increment requires an additional 6 faction sympathy so TL20 requires 12, TL30 requires 18, TL40 requires 24, and so on up to TL150 which requires 90 faction sympathy to accept the construction job.