First to clarify, which you might realize. When you open the lens (smaller number bigger hole) one need to increase the shutter speed so you always get the one single correct amount of light (based on ISO).
When in focus the lens produces a pin point of light (thousands of them all over the frame) at the exact point of focus. As the distance to subject moves away from the focus distance the point of light (circle of confusion) gets bigger. The bigger the opening in the lens the faster the CoC gets bigger (gets out of focus quicker). Therefore the bigger the hole the smaller the DOF.
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