This is all clearly covered in Section 10 the 1872 Mining Act EarthEx.
QUOTE
Sec. 10
all placer mining-claims hereafter located shall conform as near as practicable with the United States system of public land surveys and the rectangular subdivisions of such surveys, and no such location shall include more than twenty acres for each individual claimant, but where such claims cannot be conformed to legal subdivisions, survey and plat shall be made as on unsurveyed lands
If there is no survey or if you can not conform to the existing survey you will need to resort to metes and bounds.
There is public policy in place that says that claims should be as compact and regular as possible. BLM regulations discourage the use of anything but aliquot parts. Basic physics tells you that the bulk of the placer deposit is rarely actually
in the water.