Rinse and cook the sushi rice for 15 minutes on low heat. Let it sit for 15 minutes if not cooked in a rice cooker.
In a bowl, microwave the salt, sugar, and vinegar for short 15-second bursts twice until all solids are melted.
Cut the nori sheets in half. Unwrap the crab meat.
Cut the cucumber into thin sticks about 1/3 inches wide.
Peel and cut the avocado into thin sticks 1/3 inches wide like the cucumber.
Place the rice into a large bowl and mix in the vinegar mixture.
Dampen hands with water. Place the nori sheet on a bamboo mat. Place the sheet with the long side lined up with the mat's bottom.
Put 1/6th of the rice onto the nori and press to even out the rice to the edges of the sheet.
Sprinkle the rice with a small amount of sesame seeds.
Add the rest of your filling ingredients to the sheet. Add only a small portion on each sheet to avoid overstuffing.
Fold the top half of the mat over and press to make the rice compact.
Fold the bottom part as well, until the top and bottom are touching. The mat should completely wrap your roll.
Now start rolling the sushi roll away from you. The roll should be completely round.
Take off the bamboo mat and cut up your roll into 6 pieces with a damp cool knife. Then cut each roll in half crosswise.
Serve sushi within an hour for freshness.