If you look closely at the graph in the linked thread a few posts back you'll see that the number of times is dependent on the pressure used. 15 times will get you to .01ppm at 30 PSI, at 15 PSI it won't get you close and at 60 PSI you'll be there after 8 purges. PV=nRT, double the pressure in a given volume and you get twice the gas molecules therefore purging with twice the pressure will get you the same turnover in half the purge cycles.
The question is what level of O2 is acceptable. Head space O2 does not equal DO.The problem with the chart is it assumes your purge gas has zero O2, which isn't the case. Beverage CO2 is 99.9% pure, that means .1%, or 1,000PPM is not CO2. We don't know what it is but let's assume it's "air" which has 20% O2. If this is the case then your CO2 has 200ppm O2. That's the lowest you'll ever get your head space. At 15 PSI 10 purges will get you to the lowest theoretical value you can get with Beverage CO2. Medical and industrial CO2 has 5 times the level of impurities, 8 15 PSI purges will get the job done in this case.
I usually toss a couple more in, 12 purges at 15 PSI gets it done for me