There isn't one specific, universally accepted term for scattering seeds randomly on a field. However, depending on the context, you could use several phrases:

General terms:

* Broadcast seeding: This is the most common term and refers to the general process of scattering seeds over a large area, regardless of the method.

* Random seeding: This term explicitly emphasizes the randomness of the seed distribution.

* Scatter seeding: This is a more informal term that simply describes the action of scattering seeds.

Specific terms:

* Hand broadcasting: This refers to scattering seeds manually by hand.

* Mechanical broadcasting: This refers to using a machine to spread seeds, which might be more efficient but doesn't necessarily guarantee a completely random distribution.

* Overseeding: This refers to scattering seeds over an existing lawn or pasture to thicken the existing vegetation.

The best term to use will depend on the specific situation and the level of formality desired.