Trinity have seen two positive tests and already had players needing to self-isolate meaning last Thursday’s game against Leeds Rhinos was postponed.
They hope to face Hull FC on Thursday but a raft of games have already been called off since the sport resumed on August 2.
After five months of lockdown, clubs had already agreed to play midweek games in a shortened campaign due to be completed at the end of November.
But, after Hull FC, Catalans Dragons, St Helens and Warrington Wolves all also saw positive tests with Leeds Rhinos, Castleford Tigers and Salford Red Devils among clubs seeing games postponed as a result, pressure is mounting.
Carter said: “There’s been some discussion on that. We have to do the best we possibly can but ultimately there may come a point where we physically run out of available dates.
“It’s tough enough as it is at the minute going to twice per week.
“We can’t physically go to three or four games per week so there may be a point we have to decide are games going to be a nil-all draw or are we going to work on the basis however many games we’ve played, the table is decided on a percentage basis – a bit like football did. I think those discussions will become more clear in the next week or so.”
Trinity needed to see four players track and trace after previous opponents Catalans Dragons reported positive tests but two of their own players later also tested positive ahead of the Leeds game.
Carter said: “I’ve got to be honest, I don’t really know how these things work; I’m not a medical person. But it would seem that Catalans managed to transmit a couple of our players and we’ve had the track and trace as well that’s meant three or four other players had to stand down and a couple of others have for varying other reasons.
“We had to err on the side of caution which meant that game against Leeds had to be postponed. We’ve always erred on the side of caution, as we did with our decision to stand Dave Fifita down the week before, and I think that’s the right thing to do.”
Asked about the players affected, Carter added: “They’ve got symptoms and they are getting all the support they need.
“Our welfare manager, Stu Dickens, and all the medical team have done an exceptional job as nobody really knows what the answer is and we’re praying a vaccine comes along shortly that eradicates everything.
“It’s a really tricky time and I think people need to realise what players staff and administrators are having to go through just to try and make sure we get to 2021.
“We might lose a couple of games and get a few pumpings along the way but if we’re here in 2021 that’s all that matters.”
Extending the season into December is only a “slim” possibility. Carter said: “It is a really fine balancing act and I’ve great sympathy with the RFL and the Super League executive as these are not easy decisions and you are not going to make everybody happy.”
He added: “We’re trying to satisfy the broadcaster with the entertainment value we give them and have a decent play-off series and Grand Final.
“But also we have to try and make sure we don’t impact next year. We have to do that as little as possible because next year for me is all about how we bounce back.
“We have to get crowds back into the grounds and have a World Cup at the end of it so we don’t want to flog the players too much.”
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