OP is maybe talking about a plastic tote, but what really matters is how many times you can reuse it. I don't know about cardboard, but iirc for the plastic vs. canvas bag comparison I believe the break-even is on the order of 20 uses to 1. i.e. if you can use the canvas bag 20 times more than the plastic bag before discarding it, the canvas bag is less resource intensive.
" In addition, they are difficult to recycle since textile recycling in the U.S. is limited—only 15.2 percent of all textiles were recycled in 2017. As a result, a cotton bag needs to be used 7,100 times to equal the environmental profile of a plastic bag."
Looking around it seems estimates vary by a fair bit, and the one you cite is on the high end. Other estimates are in the low hundreds, which is a very attainable number of reuses. But it does seem my memory was unrealistically low. Also an aspect that is not considered in these studies is that canvas bags generally carry more stuff per bag than single use plastic ones, so taking 2 canvas bags to the grocery store can save 6 or 8 plastic bags.
The difference seems to be how far down the rabbithole you go - are you only tracking the energy to make/ship/(hopefully recycle) the bag or, as the study I linked does, goes all the way back to the plant in the field. Cotton is very water intensive.
Edit: I just realized that the word "tote" could have meant a bag of some sort. When I used to unload them everyone was calling them "totes", as in "unload that tote" and I hadn't thought about the word use until now. Though an image search for "totes" is mostly what I'm talking about: https://duckduckgo.com/?q=totes&t=ffab&iar=images&iax=images...
