The VIX is a portfolio of OTM options on the SPX with non-zero quotes.
From CBOE white-paper:
Only SPX options quoted with non-zero bid prices are used in the VIX Index calculation. [...] As volatility rises and falls, the strike price range of options with non-zero bids tends to expand and contract. As a result, the number of options used in the VIX Index calculation may vary from month-to-month, day-to-day and possibly, even minute-to-minute.
I know that the number of options changes all the time (with the weights), but I was wondering how big can this number get in practice.
NOTE: I am not interested in the feasibility of such replication or to question any economic benefits in doing it. I am working on a research thesis and I could not find any sources that give an estimate of such quantity.