Rinse the rice in three changes of cold water, rubbing the grains together to remove excess outer starch. Drain well and place in a pot with 2-1/4 cups cold water. Bring to a boil over high heat. Turn the heat to its lowest setting; over and cook until tender, about 15-18 minutes. Combine the vinegar, sugar and salt in a small pot. Bring to a boil and stir to dissolve the sugar. Remove from the heat. Spoon and spread the cooked rice into a large, shallow-sided pan. Stir in the vinegar mixture; cool the rice to room temperature.
Line an 8 x 8-inch pan with plastic wrap. Fit a piece of nori into the bottom of the pan. Spread and pack, with cold water moistened hands, 1/3 of the rice on top of the nori. Top with another sheet of nori, pressing it firmly down. Brush the top of the nori with 1/2 the mayonnaise. Top the mayonnaise with ½ the shrimp. Top the shrimp with another sheet of nori. Top the nori with a 1/3 more of the rice. Top with another sheet of nori, remaining mayonnaise and shrimp. Top the shrimp with last sheet of nori, and then the remaining rice. Press down on the rice to compact the layers. Invert the pan unto a cutting board and unmould the sushi. Cut into 24 squares. Garnish each square, if desired, with wasabi and pickled ginger. Or serve those items, and soy sauce, alongside.