The amount required will depend on several factors: the type of financing (conventional or creative), your credit rating, the amount of debt you currently have, your terms, etc.
Most conventional lenders (banks, mortgage brokers, credit unions, etc) currently require at least a 10% down-payment ($160K). If the purchase price of that home were between $271,050 and $729,750, then you might have qualified for a FHA-jumbo loan--in which case you'd only be required to put down at least 3%.
Yet, if you were to pursue creative--instead of conventional--financing, then you might have more flexibility. The key here is to negotiate with the seller to finance a portion or all of the loan amount. In fact, it might actually be easier for you to purchase a $1.6M with seller financing now in this market, because some conventional lenders are skittish about funding deals this large.