Update 7-14-2022: Reformed "tens-ones" combination option to make his system sound better: changed the sequence "-ekal, -emej, -egij, -east, -elun, -eferm, -ejov, -esol, -ebet" to "-ekal, -ej, -ij, -ast, -elun, -eferm, -ov, -ol, -et".
Update 7-15-2022: Reformed "tens-ones" combination option again to make it easier.
Here is my extended list of Tier 4 -illions, which are based on hyper-astronomical objects.
Metillion = 10^(3*10^(3*10^(3*10^45))+3) [#15]
Dettillion = 10^(3*10^(3*10^(6*10^45))+3) [#15*2]
Trettillion = 10^(3*10^(3*10^(6*10^45))+3) [#15*3]
Tettillion = 10^(3*10^(3*10^(6*10^45))+3) [#15*4]
Zeettillion = 10^(3*10^(3*10^(2.1*10^46))+3) [#15*7]
Dakettillion = 10^(3*10^(3*10^(3*10^46))+3) [#15*10]
Hotettillion = 10^(3*10^(3*10^(3*10^47))+3) [#15*100]
Xevillion = 10^(3*10^(3*10^(3*10^48))+3) [#16]
Dakevillion = 10^(3*10^(3*10^(3*10^49))+3) [#16*10]
Hotevillion = 10^(3*10^(3*10^(3*10^48))+3) [#16*100]
Hypillion = 10^(3*10^(3*10^(3*10^51))+3) [#17]
Dakypillion = 10^(3*10^(3*10^(3*10^52))+3) [#17*10]
Hotypillion = 10^(3*10^(3*10^(3*10^53))+3) [#17*100]
Omnillion = 10^(3*10^(3*10^(3*10^54))+3) [#18]
Dakomnillion = 10^(3*10^(3*10^(3*10^54))+3) [#18*10]
Hotomnillion = 10^(3*10^(3*10^(3*10^54))+3) [#18*100]
Outillion = 10^(3*10^(3*10^(3*10^57))+3) [#19]
Dakoutillion = 10^(3*10^(3*10^(3*10^57))+3) [#19*10]
Hotoutillion = 10^(3*10^(3*10^(3*10^57))+3) [#19*100]
Barrillion = 10^(3*10^(3*10^(3*10^60))+3) [#20]
Dakarrillion = 10^(3*10^(3*10^(3*10^61))+3) [#20*10]
Hotarrillion = 10^(3*10^(3*10^(3*10^62))+3) [#20*100]
Barralillion = 10^(3*10^(3*10^(3*10^63))+3) [#21]
Barrejillion = 10^(3*10^(3*10^(3*10^66))+3) [#22]
Barrijillion = 10^(3*10^(3*10^(3*10^69))+3) [#23]
Barrastillion = 10^(3*10^(3*10^(3*10^72))+3) [#24]
Barrunillion = 10^(3*10^(3*10^(3*10^75))+3) [#25]
Barrermillion = 10^(3*10^(3*10^(3*10^78))+3) [#26]
Barrovillion = 10^(3*10^(3*10^(3*10^81))+3) [#27]
Barrolillion = 10^(3*10^(3*10^(3*10^84))+3) [#28]
Barretillion = 10^(3*10^(3*10^(3*10^87))+3) [#29]
Garrillion = 10^(3*10^(3*10^(3*10^90))+3) [#30]
Dakogarrillion = 10^(3*10^(3*10^(3*10^91))+3) [#30*10]
Hotogarrillion = 10^(3*10^(3*10^(3*10^92))+3) [#30*100]
Garralillion = 10^(3*10^(3*10^(3*10^93))+3) [#31]
Garrejillion = 10^(3*10^(3*10^(3*10^96))+3) [#32]
Garrijillion = 10^(3*10^(3*10^(3*10^99))+3) [#33]
Garrastillion = 10^(3*10^(3*10^(3*10^102))+3) [#34]
Garrunillion = 10^(3*10^(3*10^(3*10^105))+3) [#35]
Garrermillion = 10^(3*10^(3*10^(3*10^108))+3) [#36]
Garrovillion = 10^(3*10^(3*10^(3*10^111))+3) [#37]
Garrolillion = 10^(3*10^(3*10^(3*10^114))+3) [#38]
Garretillion = 10^(3*10^(3*10^(3*10^117))+3) [#39]
Astarrillion = 10^(3*10^(3*10^(3*10^120))+3) [#40]
Dakastarrillion = 10^(3*10^(3*10^(3*10^121))+3) [#40*10]
Hotastarrillion = 10^(3*10^(3*10^(3*10^122))+3) [#40*100]
Astarralillion = 10^(3*10^(3*10^(3*10^123))+3) [#41]
Astarrejillion = 10^(3*10^(3*10^(3*10^126))+3) [#42]
Astarrijillion = 10^(3*10^(3*10^(3*10^129))+3) [#43]
Astarrastillion = 10^(3*10^(3*10^(3*10^132))+3) [#44]
Astarrunillion = 10^(3*10^(3*10^(3*10^135))+3) [#45]
Astarrermillion = 10^(3*10^(3*10^(3*10^138))+3) [#46]
Astarrovillion = 10^(3*10^(3*10^(3*10^141))+3) [#47]
Astarrolillion = 10^(3*10^(3*10^(3*10^144))+3) [#48]
Astarretillion = 10^(3*10^(3*10^(3*10^147))+3) [#49]
Lunarrillion = 10^(3*10^(3*10^(3*10^150))+3) [#50]
Fermarrillion = 10^(3*10^(3*10^(3*10^180))+3) [#60]
Jovarrillion = 10^(3*10^(3*10^(3*10^210))+3) [#70]
Solarrillion = 10^(3*10^(3*10^(3*10^240))+3) [#80]
Betarrillion = 10^(3*10^(3*10^(3*10^270))+3) [#90]
Betarretillion = 10^(3*10^(3*10^(3*10^297))+3) [#99]
Hutillion = 10^(3*10^(3*10^(3*10^300))+3) [#100]
Dakutillion = 10^(3*10^(3*10^(3*10^301))+3) [#100*10]
Hotutillion = 10^(3*10^(3*10^(3*10^302))+3) [#100*100]
Hutalillion = 10^(3*10^(3*10^(3*10^303))+3) [#101]
Hutejillion = 10^(3*10^(3*10^(3*10^306))+3) [#102]
Hutijillion = 10^(3*10^(3*10^(3*10^309))+3) [#103]
Hutastillion = 10^(3*10^(3*10^(3*10^312))+3) [#104]
Hulunillion = 10^(3*10^(3*10^(3*10^315))+3) [#105]
Hufermillion = 10^(3*10^(3*10^(3*10^318))+3) [#106]
Hujovillion = 10^(3*10^(3*10^(3*10^321))+3) [#107]
Husolillion = 10^(3*10^(3*10^(3*10^324))+3) [#108]
Hubetillion = 10^(3*10^(3*10^(3*10^327))+3) [#109]
Huglocillion = 10^(3*10^(3*10^(3*10^330))+3) [#110]
Hugaxillion = 10^(3*10^(3*10^(3*10^333))+3) [#111]
Husupillion = 10^(3*10^(3*10^(3*10^336))+3) [#112]
Huversillion = 10^(3*10^(3*10^(3*10^339))+3) [#113]
Humultillion = 10^(3*10^(3*10^(3*10^342))+3) [#114]
Humetillion = 10^(3*10^(3*10^(3*10^345))+3) [#115]
Huxevillion = 10^(3*10^(3*10^(3*10^348))+3) [#116]
Hutypillion = 10^(3*10^(3*10^(3*10^351))+3) [#117]
Hutomnillion = 10^(3*10^(3*10^(3*10^354))+3) [#118]
Hutoutillion = 10^(3*10^(3*10^(3*10^357))+3) [#119]
Hubarrillion = 10^(3*10^(3*10^(3*10^360))+3) [#120]
Hubarralillion = 10^(3*10^(3*10^(3*10^363))+3) [#121]
Hubarrejillion = 10^(3*10^(3*10^(3*10^366))+3) [#122]
Hubarrijillion = 10^(3*10^(3*10^(3*10^369))+3) [#123]
Hubarrastillion = 10^(3*10^(3*10^(3*10^372))+3) [#124]
Hubarrunillion = 10^(3*10^(3*10^(3*10^375))+3) [#125]
Hubarrermillion = 10^(3*10^(3*10^(3*10^378))+3) [#126]
Hubarrovillion = 10^(3*10^(3*10^(3*10^381))+3) [#127]
Hubarrolillion = 10^(3*10^(3*10^(3*10^384))+3) [#128]
Hubarretillion = 10^(3*10^(3*10^(3*10^387))+3) [#129]
Hugarrillion = 10^(3*10^(3*10^(3*10^390))+3) [#130]
Hutastarrillion = 10^(3*10^(3*10^(3*10^420))+3) [#140]
Hulunarrillion = 10^(3*10^(3*10^(3*10^450))+3) [#150]
Hufermarrillion = 10^(3*10^(3*10^(3*10^480))+3) [#160]
Hujovarrillion = 10^(3*10^(3*10^(3*10^510))+3) [#170]
Husolarrillion = 10^(3*10^(3*10^(3*10^540))+3) [#180]
Hubetarrillion = 10^(3*10^(3*10^(3*10^570))+3) [#190]
Mutillion = 10^(3*10^(3*10^(3*10^600))+3) [#200]
Dakomutillion = 10^(3*10^(3*10^(3*10^601))+3) [#200*10]
Hotomutillion = 10^(3*10^(3*10^(3*10^602))+3) [#200*100]
Mutalillion = 10^(3*10^(3*10^(3*10^603))+3) [#201]
Muglocillion = 10^(3*10^(3*10^(3*10^630))+3) [#210]
Mugaxillion = 10^(3*10^(3*10^(3*10^633))+3) [#211]
Mubarrillion = 10^(3*10^(3*10^(3*10^660))+3) [#220]
Gutillion = 10^(3*10^(3*10^(3*10^900))+3) [#300]
Astutillion = 10^(3*10^(3*10^(3*10^1200))+3) [#400]
Lutillion = 10^(3*10^(3*10^(3*10^1500))+3) [#500]
Futillion = 10^(3*10^(3*10^(3*10^1800))+3) [#600]
Jutillion = 10^(3*10^(3*10^(3*10^2100))+3) [#700]
Sutillion = 10^(3*10^(3*10^(3*10^2400))+3) [#800]
Butillion = 10^(3*10^(3*10^(3*10^2700))+3) [#900]
Bubetarrillion = 10^(3*10^(3*10^(3*10^2970))+3) [#990]
Bubetarretillion = 10^(3*10^(3*10^(3*10^2997))+3) [#999]
Dakobubetarretillion = 10^(3*10^(3*10^(3*10^2998))+3) [#999*]
Hotobubetarretillion = 10^(3*10^(3*10^(3*10^2999))+3) [#999*]
Nonecxenobubetarretillion = 10^(3*10^(3*10^(2.997*10^3000))+3) [#999*]
Tier 4 by Tier 3 limit:
Nonecxenobubetarretinonecxenobubetarrolinonecxenobubetarrovi...nonecxenijinonecxenejinonecxenalnonecxenillion = 10^(3*10^(3*10^(3*10^3000-3))+3) [#999*999+#998*999+#997*999+#996*999+#995*999+...+#5*999+#4*999+#3*999+#2*999+#1*999+#0*999]
Rise of Jonathan Bowers' -illions, there are joints of generalization methods based on his extended Tier 4 -illions! One is filling all Tier 4 -illions and let us to Tier 5 and can't keep up!
In his system, generalization of extended Tier 4 -illions is slightly different from Aarex Tiaokhiao's system, because of the large number of tweaks to the base roots and system.
Let's start with the very first difference first. You can see that the Tier 3 multiplicatives to out (outillion, 19th Tier 4 -illion) is -ut in the original generalization system by Aarex Tiaokhiao while we have -out in the generalization system here, since "o" is a vowel, hence the letter "o" will not be dropped.
For example:
[#19*3] = 10^(3*10^(3*10^(9*10^57))+3) => trutillion in the original system, but troutillion in the system here.
[#19*53] = 10^(3*10^(3*10^(1.59*10^59))+3) => pectrutillion in the original system, but pectroutillion in the system here.
[#19*111] = 10^(3*10^(3*10^(3.33*10^59))+3) => hotendutillion in the original system, but hotendoutillion in the system here.
[#19*835] = 10^(3*10^(3*10^(2.505*10^60))+3) => yootracpetutillion in the original system, but yootracpetoutillion in the system here.
Next, we can easily see the difference between the original name and his modified name for the 40th Tier 4 -illion is "aarrillion" by CompactStar, but we have "astarrillion" by me. Its tweak is due to the pronunciation and generalization problems. For example, Aarex uses oaarr for Tier 3 multiplicatives while we use astarr in the generalization system here.
Also, for ones roots added after tens roots of the Tier 4 -illions, Aarex uses only one possibility for each ones roots as follows: -ekal, -ej, -ij, -ast, -un, -erm, -ov, -esol, and -et, while in his generalization system, both forms of each ones roots are valid: -[ek]al, -[em]ej, -[eg]ij, -[e]ast, -[el]un, -[ef]erm, -[ej]ov, -[es]ol, and -[eb]et, respectively (roots in square brackets can be omitted).
Edit: 15th July: Reformed "tens-ones" combination option to make his system sound better and easier to generalize: changed the sequence "-ekal, -emej, -egij, -east, -elun, -eferm, -ejov, -esol, -ebet" to "-al, -ej, -ij, -ast, -un, -erm, -ov, -ol, -et" to match the Tier 3 multiplicatives to Tier 4:
1: -ekal => -al
2: -emej => -ej
3: -egij => -ij
4: -east => -ast
5: -elun => -un
6: -eferm => -erm
7: -ejov => -ov
8: -esol => -ol
9: -ebet => -et
Moving on hundreds, I eradicate hut into ut for Tier 3 multiplicatives to hut (100~199th Tier 4 -illion). In his generalization system this is -ohut while we have -ut in the generalization system here. In that case, take the letter "h" out and replace with the Tier 3 multiplicatives as it can be done using the same reasoning that Tier 3 multiplicatives to hypillion drops the letter "h" out, and to avoid conflict with "out", since I decided to change Tier 3 multiplicative to out from "-ut" to "-out". Also, Tier 3 multiplicatives to astut (400~499th Tier 4 -illion) will not add "o" before it as "a" is a vowel.
After that, for inter-tier additives to hundreds will be far different from the Aarex's generalization system, i.e. use "t" if it comes before ones/tens roots by the following: kal => tal, mej => tej, gij => tij, ast => tast, hyp => typ, omn => tomn, out => tout, and astarr => tastarr, respectively. These because kal, mej, and gij are not based on astronomical objects, but derived forms of the large SI prefixes; ast, omn, and out start with a vowel; and hyp must be generalized using the same reasoning as Tier 3 generalization on hundreds as in hotendillion. Otherwise, remove the last "t" if it comes before ones/tens roots.
And finally, let's see the difference for the intermediate extended Tier 4 -illions between the Aarex's generalization system and the generalization system here:
[#40*13] = 10^(3*10^(3*10^(3.9*10^121))+3) => tradakoaarrillion in the original system, but tradakastarrillion in the system here.
[#97*125] = 10^(3*10^(3*10^(3.75*10^293))+3) => hoticpetetarrovillion in both systems, but hoticpetetarrejovillion in his alternative system only.
[#419*31] = 10^(3*10^(3*10^(9.3*10^1258))+3) => trakenoastuoutillion in the original system, but trakenastutoutillion in the system here.
[#666*666+665*666] = 10^(3*10^(3*10^(1.999998*10^2001))+3) => exotexakectofufermarrermexotexakectofufermarrunillion in the original system, but exotexakectofufermarrermiexotexakectofufermarrunillion in the system here.
We can construct a very long Tier 4 -illions like (bold + underline = difference):
Aarex Tiaokhiao's original system:
one yootexacxenoastuaarrerm
yootexacxenoastuaarrun
yootexacxenoastuaarrast
yootexacxenoastuaarrijillion
DeepLineMadom's modified system:
one yootexacxenastutastarrefermi
yootexacxenastutastarreluni
yootexacxenastutastarreasti
yootexacxenastutastarregijillion
Reformation update (italic = change, scrapped in July 15), changed to:
one yootexacxenastutastarrermi
yootexacxenastutastarruni
yootexacxenastutastarrasti
yootexacxenastutastarrijillion (this is prefered)
= 10^(3*10^(3*10^(2.609 609 609 607*10^1341))+3) = (8.69 869 869 869*10^1340)-th Tier 3 -illion
And the close limit to the baseline Tier 5 -illion like:
one nonecxenobubetarrebeti
nonecxenobubetarresoli
nonecxenobubetarrejovi
nonecxenobubetarrefermillion
or
one nonecxenobubetarreti
nonecxenobubetarroli
nonecxenobubetarrovi
nonecxenobubetarrermillion (this is prefered)
= 10^(3*10^(3*10^(2.999 999 999 997*10^3000))+3) = (9.99 999 999 999*10^1340)-th Tier 3 -illion
Not only some tweaks by me, but also:
Miserly, Tier 3 additives to "yoc" (from "y" + "[gl]oc") collides with the generalized Tier 3 -illions:
y + gloc + od => yocodillion (collides with 82nd Tier 3 -illion)
y + gloc + tr => yoctrillion (collides with 83rd Tier 3 -illion)
y + gloc + ter => yocterillion (collides with 84th Tier 3 -illion)
y + gloc + pet => yocpetillion (collides with 85th Tier 3 -illion)
y + gloc + zet => yoczetillion (collides with 87th Tier 3 -illion)
y + gloc + xen => yocxenillion (collides with 89th Tier 3 -illion)
but not:
y + gloc + en => yocenillion (not to be confused with 81st Tier 3 -illion: yokenillion)
y + gloc + ect => yocectillion (not to be confused with 86th Tier 3 -illion: yokectillion))
y + gloc + yot => yocyotillion (not to be confused with 88th Tier 3 -illion: yokyotillion)
To fix them, just add "i" to connect with the lone Tier 3 root, like Sbiis Saibian! For example:
y + gloc + i + od => yociodillion
y + gloc + i + tr => yocitrillion
y + gloc + i + ter => yociterillion
y + gloc + i + pet => yocipetillion
y + gloc + i + zet => yocizetillion
y + gloc + i + xen => yocixenillion