The productivity of rice could possibly be increased by means of incorporation of genes responsible for any given conditions. That need modern molecular biological techniques.
It is important to precise the type of rice ecosystem you are interested in. In the case of irrigated rice, IRRI's Bas Bouman team and national collaborators have been studying this in China since the 90s. And in the case of upland rice you may have a look at Thomas George's article on change in yield performance over time. There may be other interesting papers on this topic from Madagascar wher CIRAD has been working on upland rice cropping systems for over 50 years. Hope it helps a bit...
Yield levels in aerobic rice and TPR-rice can be similar provided:
1. Soil texture is medium to heavy i.e. loamy - clay loam. In light soil, acute Fe deficiency appears lesding to complete failure in case of aerobic rice.
2. Field is laser levelled.
3. Rice seed should be drilled not deeper than 2-3 cm.
4. Water application is such that soil remains moist through out crop season. need not of water stagnation but can't allow cracks to appear in aerobic rice.
5. Diverse weed flora can be controlled with sequential application of pre- and post-emergence herbicides. It can be integrated with hand pulling of weeds at 70 DAS.
6. Continuous monitoring of field for any insect-pest and disease attacks.
Possible research area:
Genotypes can be developed especially for aerobic systems.
Non-flooded overhed irrigated rice was grown at Tambankulu in NE Swaziland in the 1960's. Initailly growth was good and yields were satisfactory. However after several seasons weeds became so prolific that increasing control costs made the crop economically non-viable , and the land was put into sugar cane. I do not know if this was ever systematically researched and written up but I don't thnk so.
I am sure that yield level of aerobic rice could be increased by judicious water management. Whenever possible please keep standing water (2-5 cm) for 20-25 days from PI. It will help increase yield and you will get rice yield higher than that could be achieved by puddle transplanted conventional irrigated or AWD irrigated fields. Please try and see what happens.
Maybe, if you think only about the production per plant or the yield (production per area). There are some cultivars being developed for that in Brazil, you should consult Embrapa about that.
However, it is also important think about the water productivity, since water is generally more scarce than land. In Brazil, it is estimated that flood irrigated rice fields consume 2.5 L/s/ha, and a rice field with sprinkler irrigation consume 1 L/s/ha.
So, it is possible to irrigate 2,5 ha by sprinkler irrigation with the same water of 1 ha of flood irrigation. The productivity gains by area may compensate the losses in plant productivity.