I did this recipe in a 68oz pickle jar but you can adjust proportions if you like.
Fermenting lids and weights are helpful but you can do this with stainless steel, plastic lids or a swing top like this one as it allows air out but not in. In place of a weight you will need a sanitized jar small enough to insert on top of the turnips. I like to pour a bit of avocado or extra virgin olive oil around the top to keep bacteria from getting in. Another trick is to fill a clean ziplock back with water and stuff it in. You’ll want to set it on a plate as it will leak fluids in this case.
If you do not have fermenting or swing lids, set the lid loosely and cover with a towel to keep bacteria out. Wait 3-7 days, depending on your taste.