The state highway system shall consist of an integrated network of arterials and of other public roads or bypasses serving as the major collectors therefor. No public road shall be designated as a part of the state highway system unless it meets at least one of the following requirements:

(1) Serves trips of substantial length and duration indicative of regional, state-wide, or interstate importance;

(2) Connects adjoining county seats;

(3) Connects urban or regional areas with outlying areas, both intrastate and interstate; or

(4) Serves as part of the principal collector network for the state-wide and interstate arterial public roads.