You can install the carpet before or after the baseboard. In new construction we put the baseboard down first, keeping it up about 1/2" above the sub-floor. Sometimes the new paint gets marked up a bit, so is then touched up after the carpet is laid. If installing the baseboard after the carpet is laid, pre-paint the baseboard and lay it on top of the carpet, not pushing it down too hard onto the carpet. The nail holes are then filled and touched up.
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