Use a bigger box than you think you'll need, and make sure the eggs can't bump against each other. Most broken eggs I have received were broken when the box was squashed and the eggs were smashed against each other side-to-side (which is their weakest dimension).
I wrap each egg in bubble wrap, then tape 3-4 eggs together side-by-side. The egg "logs" are then taped together in a big egg log and wrapped in big bubble wrap. I use styrofoam peanuts and I pack the box tight. The packing material will settle in transit, so use a lot. Shredded newspaper settles a lot. You want the eggs to not be able to move around at all.
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