autos are variable size, so i'll just assume you'll make it fit the 4x4 (120x120).
16 sq ft running 18hours a day will need roughly 920 umol/s PAR produced from a light -- this assumes distribution of said light is proper for a 4x4, so apply some common sense.
Any grow light that produces that much will do a great job. May even need to dim it 5-10%, but it'll be safely near max DLI for ambient CO2.
If you want to keep open the possiblity to grow photoperiods, you have to do these calculations for 12 hours of operation. It is inversely proportional, so 12h vs 18 needs 150% of the power. 1.5 * 920 = 1380 umol/S PAR.
The DLI that results from each of these suggestions is the same. This is all worked backward from 38-39 DLI calculated from full power of the light.. in reality, the plants will get less than that and that's built into these suggestions. Fairly well-controlled temp and rh will be required to hit these levels of DLI and typical ambient CO2. Relative to existing LED grow lights means the hanging distances are roughly similar. A measurement at your canopy level would be a better metric to use in the future if dynamics of grow lights change.
more power from greater distance will have better penetration -- retain higher levesl further away from the lgiht.. .this is due to light spreading out in a way that adheres to the inverse square law and not an opinion or bro-science. So, there are things to consider when choosing umol/s PAR power and distance from canopy. You can run fewer watts and much closer, but then you don't get as much light deeper into canopy. This is great in early vege, but maybe not optimal for fully grown plants.
read the wiki on DLI. It's super easy stuff to comprehend and apply. (daily light integral) .. for the most part that is the key, but as i just stated power and distance is a variable too. You need to waste more electricity from further away and up to a point that will be a benefit. LED are usually best ~18" away. Reduces hotspot in center and improves sides/corners. With a tiny plant in early vege, go ahead and amp down, get it nice and close -- use a klux meter or quantum meter and you can ensure your light at canopy is at the proper level at the lower percentage of power. when it is closer, the light has not spread out as much, so you can use less electricity and provide same DLI.
From all that, you should be able to extrapolate or deduce anything you need to do with a light.