It's rumored to be the .375Ruger.
There's a picture of a loaded round on Nosler's Facebook page. It looks very similar to a 7mm RUM, which has the .300RUM as a parent, which has the .404 Jefferey as a parent.
GunDigest has diagram with only a few dimensions. If it's to scale, the rest could be calculated.
The head diameter matches the .375Ruger exactly and the case is 0.10 longer, which a length increase would be expected from necking it down.