The European Food Safety Authority (EFSA) recommends 40 milligrams aspartame per kilogram of body weight. Since aspartame is approximately 200 times sweeter than the sugar (sucrose), then its use will involve very small amounts & research has not found harmful side effects upon using it except when taken together with some schizophrenia medications.

The correct answer is zero.

Not only is adding aspartame asking for trouble (phenylketonuria and CNS) but you have to consider that you are depositing THE WHOLE amount of aspartame on the taste buds in a very small amount of water (saliva) so that the effective concentration on the buds is infinite and the taste revolting (that applies for the API as well but it is a fact elegantly overlooked by the fans of ODT). You probably have a manureload of mannitol anyway. If you think you can "mask" the taste of the API with sweetness, you are wrong.

I strongly agree with Dr. Ali Adil and all these reported effects of Aspartame are dose related i.e. observed when used in higher doses continuously for longer period of time. In case of ODTs, Aspartame is used only to improve the taste and mouth feel of the tablets. It is not to mask the bitter taste. if any one claims to mask bitter taste using Aspartame he is totally wrong as mentioned by Mr. Daniel. 

you can determine per tablet quantity of aspartame by placebo technique using volunteers, if your drug is taste less. I have mentioned the detailed procedure, though it is for effervescent tablets but have also successfully applied for ODTs,  in my paper  entitled " Application of SeDeM experts System in Formulation Development of Effervescent tablets by direct compression".

Keep in mind Aspartame has poor flow and compressibility. In higher concentration it also produces bitter after taste.