Using the Aurora Ticket received from events on their copy of Pokémon FireRed & LeafGreen games,
players gain access to the Birth Island, and get a chance to capture the Mythical Deoxys!
Do note that the Aurora Ticket was never distributed to the Japanese copies of Pokémon Emerald Version.
For players who rather not use the Mystery Gift to activate the event, simply use PKHeX's Event Flags > Research, and
For Pokémon FireRed & LeafGreen: Check Flag 2122 and Flag 2123 , then proceed to add an Aurora Ticket into the Key Items of the Bag.
For Pokémon FireRed & LeafGreen, having the National Dex and Rainbow Pass may be required. More event flags here.