The victims were from Austria and neighboring Italy, Germany and Switzerland, and most were aged between 19 and 25 years old. Most of the assaults were committed between 11.30pm and 1.30am, and 16 of the reported cases happened in the town's market square.
"The men are said to be of Mediterranean appearance and under the age of 30. According to the victims, they were dark-haired and some of them wore a beard,” Austria's Kroner Zeitung reported.
The police investigation is ongoing, and the perpetrators are yet to be apprehended.
"We believe that these attacks were committee by the same group,” a police source told the newspaper.
"We are looking for a group of five to six men, of whom all the victims gave a similar description.”
The attackers “had a system,” and attacked the women when they had become separated from their group, the police said.
Women in several other Austrian cities have also reported sexual assaults during public celebrations on New Year's Eve.
A 31-year-old woman in Salzburg was sexually assaulted by an 18-year-old Afghan asylum seeker.
Three women in Vienna have also reported sexual assaults on New Year's Eve. One was a 16-year-old year who was molested by a taxi driver.
The attacks follow a spate of sexual assaults committed by asylum seekers in Austria over the past year. In August nine Iraqi refugees and asylum seekers were arrested as suspects in the rape of a 28-year-old woman during the early hours of January 1 2016.
In one high-profile case, a 20-year-old Iraqi refugee raped a ten-year-old boy at a swimming pool in Vienna. The man was sentenced in June but his conviction was later overturned after supreme court judges said they could not establish whether he believed the child consented, and he faces a retrial next year.
Last month the Austrian newspaper Kurier reported that the number of sex attacks committed by migrants in Austria more than doubled during 2016. According to interior ministry statistics, in 2015 asylum seekers in Austria committed 39 rapes. Over the first nine months of 2016 the number of asylum seekers under investigation for rape increased to 91, an increase of 133 percent in comparison with the figure for the 12 months previously.
Among asylum seekers, the highest proportion of suspected rapists were from Afghanistan, and the number of Afghan asylum seekers suspected of rape increased from 16 in 2015 to 47 between January and September 2016,