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Giggolunex
100000.....00000    100

100000.....00000

100000.....00000
100000.....00000
10000000000
Giggolunex in zeroes

Giggolunex is equal to s(10,giggol) = s(10,s(10,100,2)) = s(10,101,2) using strong array notation, or $$10\uparrow\uparrow101$$ or 10110.[1] The term was coined by Aarex Tiaokhiao. It is equal to 1 followed by giggol zeroes. It can also be called Googolplexin-Giggol.[2]

Username5243 calls this number Doogolunex, and it's equal to 10[1]10[2]100 = 10[2]101 in Username5243's Array Notation.[3]

Approximations in other notations

Notation Approximation
Arrow notation $$10 \uparrow\uparrow 101$$ (exact)
Hyper-E notation $$\textrm{E}1\#101$$
$$=\textrm{E}10\#100$$
Chained arrow notation $$10 \rightarrow 101 \rightarrow 2$$ (exact)
BEAF $$\{10,101,2\}$$ (exact)
Bird's array notation $$\{10,101,2\}$$ (exact)
Hyperfactorial array notation $$101!1$$
Fast-growing hierarchy $$f_3(100)$$
Hardy hierarchy $$H_{\omega^3}(100)$$
Slow-growing hierarchy $$g_{\varepsilon_0}(101)$$

Sources

1. Part 1 (LAN) - Aarex Googology (archived)
2. Tiaokhiao, Aarex. Aarex's Googology - SAN. Retrieved 2021-03-17.
3. Username5243. Part 1 - My Large Numbers. Retrieved 2017-01-15.