Here is my numbers using Phenol notation. Note that numbers in asterisk are not by me.

Members: 218

Basic array series

Googol regiment

(1*) Googol = 10[1]100

(2*) Googolplex = 10[1]10[1]100

(3*) Googolduplex = 10[1]10[1]10[1]100

(4*) Googoltriplex = 10[1]10[1]10[1]10[1]100

(5*) Googolquadriplex = 10[1]10[1]10[1]10[1]10[1]100

(6*) Googolquintiplex = 10[1]10[1]10[1]10[1]10[1]10[1]100

(7*) Googolsextiplex = 10[1]10[1]10[1]10[1]10[1]10[1]10[1]100

(8*) Googolseptiplex = 10[1]10[1]10[1]10[1]10[1]10[1]10[1]10[1]100

(9*) Googoloctiplex = 10[1]10[1]10[1]10[1]10[1]10[1]10[1]10[1]10[1]100

(10*) Googolnoniplex = 10[1]10[1]10[1]10[1]10[1]10[1]10[1]10[1]10[1]10[1]100

(11*) Googoldeciplex = 10[1]10[1]10[1]10[1]10[1]10[1]10[1]10[1]10[1]10[1]10[1]100

(85*) Monologue = 10[2]1 = 10

(86*) Dialogue = 10[2]2 = 10[1]10 = 10^10 = 10,000,000,000

(87*) Trialogue = 10[2]3 = 10[1]10[1]10 = 10^10^10 = 10^10,000,000,000 = 10^^3

(88*) Tetralogue = 10[2]4 = 10[1]10[1]10[1]10 = 10^10^10^10 = 10^10^10,000,000,000 = 10^^4

(89*) Pentalogue = 10[2]5 = 10[1]10[1]10[1]10[1]10 = 10^10^10^10^10 = 10^^5

(90*) Hexalogue = 10[2]6 = 10[1]10[1]10[1]10[1]10[1]10 = 10^10^10^10^10^10 = 10^^6

(91*) Heptalogue = 10[2]7 = 10[1]10[1]10[1]10[1]10[1]10[1]10 = 10^10^10^10^10^10^10 = 10^^7

(92*) Octalogue = 10[2]8 = 10[1]10[1]10[1]10[1]10[1]10[1]10[1]10 = 10^10^10^10^10^10^10^10 = 10^^8

(93*) Ennalogue = 10[2]9 = 10[1]10[1]10[1]10[1]10[1]10[1]10[1]10[1]10 = 10^10^10^10^10^10^10^10^10 = 10^^9

(94*) Dekalogue = 10[2]10 = 10[1]10[1]10[1]10[1]10[1]10[1]10[1]10[1]10[1]10 = 10^10^10^10^10^10^10^10^10^10 = 10^^10

(95*) Endekalogue = 10[2]11 = 10^^11

(96*) Dodekalogue = 10[2]12 = 10^^12

(97*) Triadekalogue = 10[2]13 = 10^^13

(98*) Tetradekalogue = 10[2]14 = 10^^14

(99*) Icosalogue = 10[2]20 = 10^^20

(100*) Triantalogue = 10[2]30 = 10^^30

(101*) Terantalogue  = 10[2]40 = 10^^40

(102*) Hectalogue = 10[2]100 = 10^^100

(103*) Chilialogue = 10[2]1,000 = 10^^1,000

(104*) Myrialogue = 10[2]10,000 = 10^^10,000

Doogol regiment

(12) Doogol = 10[2]100 = 10^^100

(13) Doogolplex = 10[2]10[2]100

(14) Doogolduplex = 10[2]10[2]10[2]100

(15) Doogoltriplex = 10[2]10[2]10[2]10[2]100

(16) Doogolquadriplex = 10[2]10[2]10[2]10[2]10[2]100

(17) Doogolquintiplex = 10[2]10[2]10[2]10[2]10[2]10[2]100

(105*) Tria-taxis = 10[3]3 = 10[2]10[2]10 = 10^^10^^10 = 10^^^3

(106*) Tetra-taxis = 10[3]4 = 10[2]10[2]10[2]10 = 10^^10^^10^^10 = 10^^^4

(107*) Penta-taxis = 10[3]5 = 10^^^5

(108*) Hexa-taxis = 10[3]6 = 10^^^6

(109*) Hepta-taxis = 10[3]7 = 10^^^7

(110*) Octa-taxis = 10[3]8 = 10^^^8

(111*) Enna-taxis = 10[3]9 = 10^^^9

(112*) Deka-taxis = 10[3]10 = 10^^^10

(113*) Hecta-taxis = 10[3]100 = 10^^^100

Troogol regiment

(18) Troogol = 10[3]100

(19) Troogolplex = 10[3]10[3]100

(20) Troogolduplex = 10[3]10[3]10[3]100

(21) Troogoltriplex = 10[3]10[3]10[3]10[3]100

(114*) Tria-petaxis = 10[4]3 = 10[3]10[3]10 = 10^^^10^^^10 = 10^^^^3

(115*) Tetra-petaxis = 10[4]4 = 10[3]10[3]10[3]10 = 10^^^10^^^10^^^10 = 10^^^^4

(116*) Deka-petaxis = 10[4]10 = 10^^^^10

(117*) Hecta-petaxis = 10[4]100 = 10^^^^100

Teroogol regiment

(22) Teroogol = 10[4]100

(23) Teroogolplex = 10[4]10[4]100

(24) Teroogolduplex = 10[4]10[4]10[4]100

(25) Teroogoltriplex = 10[4]10[4]10[4]10[4]100

(118*) Deka-exaxis = 10[5]10 = 10^^^^^10

(123*) Hecta-exaxis = 10[5]100 = 10^^^^^100

Petoogol regiment

(26) Petoogol = 10[5]100

(27) Petoogolplex = 10[5]10[5]100

(28) Petoogolduplex = 10[5]10[5]10[5]100

(29) Petoogoltriplex = 10[5]10[5]10[5]10[5]100

(119*) Deka-eptaxis = 10[6]10 = 10^^^^^^10

(124*) Hecta-eptaxis = 10[7]10 = 10^^^^^^100

Ectoogol regiment

(30) Ectoogol = 10[6]100

(31) Ectoogolplex = 10[6]10[6]100

(32) Ectoogolduplex = 10[6]10[6]10[6]100

(33) Ectoogoltriplex = 10[6]10[6]10[6]10[6]100

(120*) Deka-octaxis = 10[7]10 = 10^^^^^^^10

(125*) Hecta-octaxis = 10[7]100 = 10^^^^^^^100

Zettoogol regiment

(34) Zettoogol = 10[7]100

(35) Zettoogolplex = 10[7]10[7]100

(36) Zettoogolduplex = 10[7]10[7]10[7]100

(37) Zettoogoltriplex = 10[7]10[7]10[7]10[7]100

(121*) Deka-ennaxis = 10[8]10 = 10^^^^^^^^10

Yottoogol regiment

(38) Yottoogol = 10[8]100

(39) Yottoogolplex = 10[8]10[8]100

(40) Yottoogolduplex = 10[8]10[8]10[8]100

(41) Yottoogoltriplex = 10[8]10[8]10[8]10[8]100

(122*) Deka-dekaxis = 10[9]10 = 10^^^^^^^^^10

Brontoogol regiment

There is the Cookie Fonster's extended SI prefix hoaxordinary realms...

(42) Brontoogol = 10[9]100

(43) Brontoogolplex = 10[9]10[9]100

(44) Brontoogolduplex = 10[9]10[9]10[9]100

Geopoogol regiment

(84) Decens = 10[10]10 = 10[0,1]10

(45) Geopoogol = 10[10]100

(46) Geopoogolplex = 10[10]10[10]100

(47) Geopoogolduplex = 10[10]10[10]10[10]100

(48) Gea'hepoogol = 10[11]100

(49) Gea'ottoogol = 10[12]100

(50) Gea'neatoogol = 10[13]100

(51) Gea'deatoogol = 10[14]100

(52) Gea'unatoogol = 10[15]100

(53) Gea'entoogol = 10[16]100

(54) Gea'fitoogol = 10[17]100

(55) Gea'sytoogol = 10[18]100

(56) Gea'brontoogol = 10[19]100

(57) Amosoogol = 10[20]100

(58) Ama'hepoogol = 10[21]100

(59) Ama'ottoogol = 10[22]100

(60) Ama'neatoogol = 10[23]100

(61) Ama'deatoogol = 10[24]100

(62) Ama'unatoogol = 10[25]100

(63) Ama'entoogol = 10[26]100

(64) Ama'fitoogol = 10[27]100

(65) Ama'sytoogol = 10[28]100

(66) Ama'brontoogol = 10[29]100

(67) Haproogol = 10[30]100

(68) Kyroogol = 10[40]100

(69) Pijoogol = 10[50]100

(70) Saganoogol = 10[60]100

(71) Pectroogol = 10[70]100

(72) Nisaboogol = 10[80]100

(73) Zotzoogol = 10[90]100

(74) Alphoogol = 10[100]100

(75) Betoogol = 10[200]100

(76) Gammoogol = 10[300]100

(77) Deltoogol = 10[400]100

(78) Thetoogol = 10[500]100

(79) Iotoogol = 10[600]100

(80) Kappoogol = 10[700]100

(81) Lambdoogol = 10[800]100

(82) Sigmoogol = 10[900]100

(83) Omegoogol = 10[1,000]100

Linear array series

Two-entry series

(126) Hectens = 10[0,1]100 = 10[100]10

(127) Decensplex = 10[0,1]10[0,1]10 = 10[0,1]10[10]10 = 10[1,1]3

(128) Decensdulex = 10[0,1]10[0,1]10[0,1]10 = 10[1,1]4

(129) Hectensplex = 10[0,1]10[0,1]100 = 10[0,1]10[100]10

(130) Hectensduplex = 10[0,1]10[0,1]10[0,1]100

(131) Decenstriplex = 10[0,1]5

(132) Expandecens = 10[1,1]10

(133) Expandhectens = 10[1,1]100

(134) Expandecensplex = 10[1,1]10[1,1]10

(135) Expandhectensplex = 10[1,1]10[1,1]100

(136) Multiexpandecens = 10[2,1]10

(137) Powerexpandecens = 10[3,1]10

(138) Teraexpandecens = 10[4,1]10

(139) Petaexpandecens = 10[5,1]10

(140) Exaexpandecens = 10[6,1]10

(141) Zettaexpandecens = 10[7,1]10

(142) Yottaexpandecens = 10[8,1]10

(143) Duedecens = 10[0,2]10 = 10[10,1]10

(144) Duedecensplex = 10[0,2]10[0,2]10

(145) Exploduedecens = 10[1,2]10

(146) Multiexploduedecens = 10[2,2]10

(147) Powerexploduedecens = 10[3,2]10

(148) Teraexploduedecens = 10[4,2]10

(149) Tristo-decens = 10[0,3]10 = 10[10,2]10

(150) Detonatristo-decens = 10[1,3]10

(151) Multidetonatristo-decens = 10[2,3]10

(152) Teristo-decens = 10[0,4]10 = 10[10,3]10

(153) Detonateristo-decens = 10[1,4]10

(154) Petisto-decens = 10[0,5]10 = 10[10,4]10

(155) Ectisto-decens = 10[0,6]10 = 10[10,5]10

(156) Zettisto-decens = 10[0,7]10 = 10[10,6]10

(157) Yottisto-decens = 10[0,8]10 = 10[10,7]10

(158) Brontisto-decens = 10[0,9]10 = 10[10,8]10

(159) Geopisto-decens = 10[0,10]10 = 10[10,9]10

Higher linear series

(160) Dis-decens = 10[0,0,1]10 = 10[0,10]10 = 10[10,9]10

(161) Dis-hectens = 10[0,0,1]100 = 10[0,100]10

(162) Dis-decensplex = 10[0,0,1]10[0,0,1]10

(163) Disya-hepe-decens = 10[1,0,1]10

(164) Disya-otte-decens = 10[2,0,1]10

(165) Disya-neate-decens = 10[3,0,1]10

(166) Disya-hapa-decens = 10[0,1,1]10 = 10[10,0,1]10

(167) Disya-hapa-hepe-decens = 10[1,1,1]10

(168) Disya-ottahapa-decens = 10[0,2,1]10 = 10[10,1,1]10

(169) Disya-neatahapa-decens = 10[0,3,1]10

(170) Disya-deatahapa-decens = 10[0,4,1]10

(171) Ottadis-decens = 10[0,0,2]10 = 10[0,10,1]10

(172) Ottadisya-hepe-decens = 10[1,0,2]10

(173) Ottadisya-hapa-decens = 10[0,1,2]10

(174) Ottadisya-ottehapa-decens = 10[0,2,2]10

(175) Neatadis-decens = 10[0,0,3]10 = 10[0,10,2]10

(176) Deatadis-decens = 10[0,0,4]10

(177) Unatadis-decens = 10[0,0,5]10

(178) Entadis-decens = 10[0,0,6]10

(179) Fitadis-decens = 10[0,0,7]10

(180) Sytadis-decens = 10[0,0,8]10

(181) Tris-decens = 10[0,0,0,1]10 = 10[0,0,10]10

(182) Tris-hectens = 10[0,0,0,1]100 = 10[0,0,100]10

(183) Tris-decensplex = 10[0,0,0,1]10[0,0,0,1]10

(184) Trisya-hepe-decens = 10[1,0,0,1]10

(185) Trisya-hapa-decens = 10[0,1,0,1]10

(186) Trisya-dis-decens = 10[0,0,1,1]10

(187) Ottetris-decens = 10[0,0,0,2]10

(188) Neatatris-decens = 10[0,0,0,3]10

(189) Deatatris-decens = 10[0,0,0,4]10

(190) Tetrakis-decens = 10[0,0,0,0,1]10

(191) Ottatetrakis-decens = 10[0,0,0,0,2]10

(192) Pentakis-decens = 10[0,0,0,0,0,1]10 = 10[0{1}1]5

(193) Hexakis-decens = 10[0,0,0,0,0,0,1]10 = 10[0{1}1]6

(194) Heptakis-decens = 10[0,0,0,0,0,0,0,1]10 = 10[0{1}1]7

(195) Octakis-decens = 10[0,0,0,0,0,0,0,0,1]10 = 10[0{1}1]8

(196) Enneakis-decens = 10[0,0,0,0,0,0,0,0,0,1]10 = 10[0{1}1]9

(197) Decakis-decens = 10[0,0,0,0,0,0,0,0,0,0,1]10 = 10[0{1}1]10

Dimensional array series

(198) Redonahlah = 10[0{1}1]10 = 10[0,0,0,0,0,0,0,0,0,0,1]10

(199) Redonahlah-hects = 10[0{1}1]100

(200) Redonahlahplex = 10[0{1}1]10[0{1}1]10

(201) Redonah-hep = 10[1{1}1]10

(202) Redonah-ott = 10[2{1}1]10

(203) Redonah-neat = 10[3{1}1]10

(204) Redonah-deat = 10[4{1}1]10

(205) Redonah-hapax = 10[0,1{1}1]10

(206) Redonah-hapa-hep = 10[1,1{1}1]10

(207) Redonah-ottapax = 10[0,2{1}1]10

(208) Redonah-neatapax = 10[0,3{1}1]10

(209) Redonah-dis = 10[0,0,1{1}1]10

(210) Redonah-ottadis = 10[0,0,2{1}1]10

(211) Redonah-tris = 10[0,0,0,1{1}1]10

(212) Redonah-tetrakis = 10[0,0,0,0,1{1}1]10

(213) Ottaredonahlah = 10[0{1}2]10

(214) Ottaredonah-hep = 10[1{1}2]10

(215) Ottaredonah-hapax = 10[0,1{1}2]10

(216) Ottaredonah-dis = 10[0,0,1{1}2]10

(217) Neataredonahlah = 10[0{1}3]10

(218) Deataredonahlah = 10[0{1}4]10