This network was previously owned by TelstraClear, which Vodafone bought last year.
Yesterday afternoon Vodafone issued a statement saying it would defend the campaign: "We stand behind the Vodafone SuperNet campaign.
"We are confident in what we are communicating and we will be defending Vodafone SuperNet in court."
A High Court telephone conference took place yesterday afternoon where it is understood timetabling for the case was discussed.
Last night the Vodafone Super-Net ad campaign was still active online.
In November last year Vodafone was fined $960,000 for what was the latest in a string of misleading advertising prosecutions brought by the Commerce Commission.
The 21 charges related to claims made by Vodafone regarding the extent of the coverage of its wireless broadband network, made in the "broadband everywhere" campaign.
Telecom admitted breaching the Fair Trading Act after misleading customers about the amount of broadband data they had used.
It reached a settlement with the Commerce Commission over the breach, which came about when inaccurate readings were used for around 97,000 customer accounts between November 2010 and June 2011 - caused by a software fault in its meters.
This story has been changed from a previous version which incorrectly said Vodafone admitted breaching the Fair Trading Act after making inaccurate meter readings. This was in fact Telecom.