The optimal solution is

>! 1, 8, 13, 58, 169, 295, 831, 1036

This set of coins allows N =

>! 3485

This set of coins is given in this paper: [Some Extremal Postage Stamp Bases](https://cs.uwaterloo.ca/journals/JIS/VOL13/Challis/challis6.html), by Michael F. Challis and John P. Robinson.

This paper was found by @alephalpha.