AT THE OTHER END of Billy Carter's Libyan connection is . . . Libya, pound for pound the nastiest regime going. No leader currently in power has tried harder to hurt American international interests, and has used more unfair tactics, than Col. Muammar Qaddafi. He has sponsored campaigns of terrorism in a dozen-plus countries and armed intervention in as many more. He has used the influence flowing from Libya's huge oil revenues and its radical ideology to fight against the Camp David peace process. He has served widely as a Soviet surrogate, doing the Kremlin's dirty work freely, even while he professes to be acting in the name of a pure Islamic doctrine. It is only the mutual interest in Libya's sale to the United States of 600,000 barrels of low-sulphur oil a day that accounts for the fact that the two countries have any official ties at all.

There are those who are attracted either by Col. Qaddafi's particular brand of Islam or by his central obsession, to destroy Israel, and who say that when you get to know him he's really quite a pleasant and reasonable fellow. Since we haven't met the colonel, we can't speak to that. In any event, it's often added-as though the erraticism of some young Third World leaders needs to be indulged -- that the really heavy stuff is pretty much in the past. That, however, is a proposition open to inspection. A former American diplomat name Henry Schuler examined it in this newspaper's Outlook section last Sunday.

Just in the first half of 1980, Mr. Schuler reported, Libya has: 1) tried to assassinate Egypt's Anwar Sadat, 2) instigated unrest in Algeria, 3) sponsored a raid into Tunisia, 4) burned the French and British embassies (after burning the American Embassy,) 5) armed Polisario guerrillas fighting Morocco, 6) enabled Moslem rebels to fight the Philippine government, 7) dispatched tribesmen to resume the civil war in Chad, 8) financed Ethiopia's Soviet arms and 9) killed exiled political foes in at least five countries.

But the point of this recital is not merely to characterize Col. Qaddafi. It is underline the American interest in keeping relations with his rogue regime under the tightest political control. Dealing with Libya is no job for free lances. President Carter had a duty to keep an errant brother at arm's length so that the already sensitive and burdened Libyan-American relationship would not be further tried.