Operations Specifications (OPSPECS) are the specifications that the FAA assigns to airlines for such things as authorized routes, types of equipment, VFR and IFR operations, and alternate requirements.
OPS Spec C055 discusses the requirement for alternate airports.
One area that is sometimes difficult for new Part 121 pilots to comprehend is the exclusivity of takeoff minimums from landing minimums. Try to picture each as completely separate from the other. Just because a particular airport is below landing minimums doesn’t (necessarily) mean you can’t depart. Instead, first attempt to consider the takeoff minimums by themselves. If the weather, airport equipment, aircraft capabilities, and FARs/Ops Specs will permit such a takeoff, nothing prevents you from departing. Only after you’ve examined the feasibility of a takeoff should you look at the landing minimums.
What if the airport is below landing mins? Then you’re required to have a takeoff alternate as outlined in 14 CFR 121.617. The exact weather mins for the takeoff alternate will be specified in the Ops Specs. In nearly all cases, your company Ops Specs will state the engine-inop, still-air distance in nautical miles (NMs); thus giving you an idea of the acceptable radius for an appropriate alternate.
121.617b says the takeoff alternate has to meet the alternate minimums in the Ops Specs. Paragraph C55 is the create your own minimums paragraph based on the available approaches. Pretty much for one approach add 400 and 1 to the mins and for 2 approaches, 200 and a half to the higher minimuns. The approaches have to be to different runways unless you're ETOPS, then they have to be to separate runways. If you're good for CAT III and the airport has dual CAT III runways you can get your alternate minimums down to 200/1800RVR. If it was down to that, I'd see about having a second alternate added to the release.