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## Higher-order legionsEdit

These numbers can be defined or approximated only using higher-order analogues of legions, in which Bowers' dubbed them (from ascending order) lugions, lagions, ligions, etc. He also used the L notation to devise analogues of arbitrarily high order.

• BIGG, 200?
• Goshomity, $$\lbrace L2,100\rbrace_{100,100} = \lbrace 100,100 \underbrace{\backslash\backslash\backslash\cdots\backslash\backslash\backslash}_{100} 2\rbrace$$
• Good goshomity, $$\{100,100 \underbrace{\backslash\backslash\backslash\backslash\ldots\backslash\backslash\backslash\backslash}_{\text{Goshomity}} 2\}$$
• Big Bukuwaha, $$\lbrace L2,X\rbrace_{100,100}$$, where X is a Bukuwaha array.
• Bongo Bukuwaha, $$\lbrace L3,X\rbrace_{100,100}$$, where X is a Big Bukuwaha array.
• Quabinga Bukuwaha, $$\lbrace L4,X\rbrace_{100,100}$$, where X is a Bongo Bukuwaha array.
• Meameamealokkapoowa, $$\{\text{L}100,10\}_{10,10}$$
• Meameamealokkapoowa-arrowa, $$\{\text{meameamealokkapoowa},2,1,2\}$$
• Meameamealokkapoowa oompa, $$\{LLL \ldots A \ldots LLL,10\}_{10,10}$$, A is a meameamealokkapoowa array of L's

## Beyond BEAFEdit

These numbers are currently beyond all levels of BEAF ever defined (even those not completely defined or in progress). They are the largest known computably large numbers devised. Numbers generated by Finite promise games and the Greedy clique sequence may also belong to this group.