Mar Rabba Gaon was the head of the yeshiva in Pumbedita around year 4430. [Shada"k pages 36 and 58b writes that Mar Huna was head of the yeshiva in Sura and Mar Rabba was head of the yeshiva in Pumbedita, and they received from Rav Yitzchak as in year 4370. Rash"b Yuchsin wrote that in his days they instituted giving a get immediately to a woman who has not heard the public declaration of the prohibition by Rav Zevid.

And in his days there was in Sura Rav Sheshna who wrote about its stringencies, Mesharsheya bar Tachlifa. And in Yuchsin in the order of tradition that the Rama"n copied, he wrote that Rav Sheshna was called Rav Mesharsheya and died in year 4442. And in Shada"k page 36b, Rav Shishna died in year 4449].

Rav Shina'na Mesharsheya bar Chalifta ruled in Sura from year 4430 for 19 years until year 4449. [And in my opinion, he is Rav Sheshna mentioned above].