Were all the Halo rings built during the Flood war?

Were the Halo rings all built in the last years of the Forerunner Empire?

Seven are recalled as belonging to the later period and eleven larger rings to an earlier one, but the chronology is explicitly uncertain.

A viewer places the rings in the Forerunners' final years. A competing recollection distinguishes seven later rings from eleven larger predecessors. That distinction is offered from memory and could be wrong. Contradictions in the fictional background prevent a firm construction chronology here.