Generation 7 update
These 54 eggs are tied at 120 cycles and 30720 steps, even though none of their eggs are obtainable.
Mewtwo, Mew, Lugia, Ho-Oh, Celebi, Latias, Latios, Kyogre, Groudon, Rayquaza, Jirachi, Deoxys, Dialga, Palkia, Regigigas, Giratina, Cresselia, Darkrai, Shaymin, Arceus, Victini, Tornadus, Thundurus, Reshiram, Zekrom, Landorus, Kyurem, Meloetta, Genesect, Xerneas, Yveltal, Zygarde, Hoopa, Volcanion, Type: Null, Silvally, Cosmog, Cosmoem, Solgaleo, Lunala, Nihilego, Buzzwole, Pheromosa, Xurkitree, Celesteela, Kartana, Guzzlord, Necrozma, Magearna, Marshadow, Poipole, Naganadel, Stakataka, Blacephalon, Zeraora
Of the eggs that are obtainable, these 20 are tied at 40 cycles and 10240 steps.
Happiny, Chansey, Lapras, Munchlax, Snorlax, Dratini, Larvitar, Wailmer, Relicanth, Bagon, Beldum, Gible, Phione, Basculin, Alomomola, Axew, Deino, Larvesta, Goomy, Jangmo-O
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