I'm not sure if you're saying it shoots a group 16 inches wide, or if it shoots 16 inches to the side of a bore sighted zero? If it's shooting either though, I've found N.E.F./H&R to always be very good about customer support and service, call them and see if sending it in for inspection is in order. I'd also check the crown for any wear or nicks to the rifleing. The forearm bedding is as said often an issue, as is resting the forarm on something hard. Most generally it seems best to rest the forarm on an open hand or a sandbag. Does it shoot such groups if you let the barrel cool between shots? If so it's a forearm issue. If not look at the crown and the reciever fit. Have you cleaned the bore of any grease, copper or leading?
If the issue is it shooting so far off from the boresighted zero, there are many rings which allow you compensate for misalignment, but I'd remove and remount everything first, maybe a good idea anyway. Lap the rings unless they're burris with the inserts, keep the right ring caps with the right ring lower halves. I had a Hornet barrel that was pitted and the factory replaced as they said they made some barrels way back that were of bad steel, is yours old or newer? Best of luck.