A eligible ticket (as indicated by the *) means that you cannot use a codeshare flight. For example, AA puts its AA designator on JAL flights to New York. It is marketed by a oneworld member but not operated by a oneworld member -- therefore it is not eligible. However, if it is an AA flight on a Quantas plane, it would qualify as flying on AA (not Quantas -- so be careful) and be an eligible ticket.

--Jim