As soon as you can - update Dog Lost website with his details.
Ring all the local vets as soon as they're open, even ones you don't use and ones not in your immediate town.
Find out the dog warden details for your area and let them know AND find out the details for any stray pounds in your area and just outside it and let them know, ideally with a photo not just a description.
Make a note of who you have called and spoken to and when - keep calling, do NOT rely on people to pass on messages or leave accurate notes, unfortunately dogs have died or been rehomed to other people this way.
Post on local FB groups - the best way if you can is to make a post on your own timeline, and then share that post to local groups. That way you have control over the post and when (fingers x) your dog IS found, you can simply update that post and it will update all the shares of it (or delete it, and ditto, all the shares will go too).
Make sure any such post has location last seen, date, time etc on it - far too many people are stressed and panicking and as a result send out lost posts that do not contain sufficient detail which just leads to further confusion.
Get your partner to go back to where he last saw the dog - if possible, leave some dirty laundry there or urine, this can really help a missing dog return and stay.
Many dogs when panicked and running will seemingly forget their people VERY quickly, do not chase your dog if they don't seem to respond to your call - sit down if you can and wait, this is much more likely to get your dog to approach you.
SIT is always worth a try however, a fleeing or panicking dog may not come back, but may respond to a sit cue as it is generally the first thing they ever learned and the strongest thing they remember.
Fingers x!