It will be after the rest of the games are played anyway, which is next Monday/Tuesday.
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It's nice to be the next round of a competition when most of the current round still has to be played.
http://www.eircomloi.ie/other-compet...ason/fixtures/
Even though there are four all-Premier Division matches, there should still be 7PD clubs in the 1/4 Finals. If I had to chose opponents I wouldn't mind the winners of Wexford Youths and Kerry League tie away (maybe benefit from a home draw later).
They are also the only two teams to shock opponents in Divisions above them. I think if a small club is going to do well this year, another shock is needed in this round.