Rinse the sushi rice thoroughly in cold water until the water runs clear. Cook the rice according to the package instructions.
In a small saucepan, combine the rice vinegar, sugar, and salt. Heat over low heat until the sugar and salt are dissolved, then pour the mixture over the warm rice and gently mix. Let it cool completely.
Slice the tuna into thin strips. Cut the cucumber and avocado into long, thin strips as well.
Place a nori sheet on a sushi bamboo rolling mat, shiny side down. Spread a thin layer of rice evenly over the nori sheet, leaving about 1-2 cm free at the top edge.
Place a strip of tuna, cucumber, and avocado in the center of the rice. Add a small amount of wasabi if you like a spicier flavor.
Using the bamboo rolling mat, tightly roll up the sushi. With a sharp knife, cut the roll into equal-sized pieces.
Serve the sushi pieces with soy sauce, wasabi, and pickled ginger.
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