A law made by local government and public corporation and empowered by an Act of Parliament is

A law made by local government authorities or public corporations under the authority granted to them by an Act of Parliament is called a bye-law (also spelt by-law).

Bye-laws are a form of delegated or subsidiary legislation. Parliament passes an enabling Act that grants specific bodies - such as local government councils and public corporations - the power to make rules and regulations within their areas of jurisdiction. These bye-laws deal with local matters such as sanitation, market regulations, traffic management, building codes, and other issues that affect the specific locality or organisation.

The other options represent different legal concepts:

• An edict is a law or decree made by a military governor. In Nigeria, edicts were the laws enacted by state military governors during periods of military rule.
• A public bill is a proposed law introduced in the legislature that affects the general public and the country as a whole.
• A private bill is a proposed law introduced in the legislature that affects a specific individual, organisation, or locality, rather than the general public.

The key feature of bye-laws is that they derive their authority from a parent Act of Parliament and operate only within the limited area or domain of the body that made them.