Wrexham will host former finalists Wigan on their return to the Carabao Cup.
The Welsh side, who will be participating in the competition for the first time since 2007-08 following their promotion to League Two, were paired with the 2006 runners-up in Thursday's first-round draw.
Notts County, who came up from the National League along with Wrexham, were handed a home tie against Lincoln.
Leicester, Leeds and Southampton must play in the first round following their relegation from the Premier League.
Leeds will host Shrewsbury, the Foxes will head across the midlands to Burton and Southampton will travel to Gillingham.
The ties will be played in the week beginning August 7. The first-round draw, featuring sides from the Championship, League One and League Two, was split into northern and southern sections.
The majority of top-flight sides will enter in the second round with those involved in European competitions going straight through to the third round.
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