How much discretion does the council have in fixing that date?

G.S. 160A-103 directs that the referendum be held on a date permitted by G.S. 163-287. That statute specifies the only times that referendums may be held: (1) at the same time as any state or county general election (even-number years only); (2) at the same time as a primary election in even-numbered years; (3) at the same time as any other election requiring all the precincts in the country to be open; and (4) at the same time as a municipal general election. The statute says that the council is "encouraged to set a date that will result in the highest voter turnout."