Why are oceans said to have "low productivity" in terms of photosynthesis?
First, we have to know which are the most important criteria for photosynthesis to occur; these are: light, CO2, water, nutrients.
docenti.unicam.it/tmp/2619.ppt
Second, the productivity, you are talking about, it should be called "primary productivity" and it is calculated, dividing the amount of carbon converted per area (m2) by the time.
ww2.unime.it/snchimambiente/PrPriFattMag.doc

So, thanks to the fact that oceans occupy the larger area of the world, the marine microorganisms can convert lots of inorganic carbon into organic (principle of photosynthesis).
A big problem in the oceans is availability of nutrients; these tend to deposit or react with water or other chemical compounds, even though the marine photosynthetic organisms are essentially found on the surface, where, of course, light is present. This reduces as a consequence the  photosynthetic productivity potential of oceans.