Best Known (90, s)-Sequences in Base 27
(90, 323)-Sequence over F27 — Constructive and digital
Digital (90, 323)-sequence over F27, using
- t-expansion [i] based on digital (72, 323)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 72 and N(F) ≥ 324, using
- F4 from the tower of function fields by Bezerra, GarcÃa, and Stichtenoth over F27 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 72 and N(F) ≥ 324, using
(90, 324)-Sequence over F27 — Digital
Digital (90, 324)-sequence over F27, using
- t-expansion [i] based on digital (48, 324)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 48 and N(F) ≥ 325, using
(90, 2400)-Sequence in Base 27 — Upper bound on s
There is no (90, 2401)-sequence in base 27, because
- net from sequence [i] would yield (90, m, 2402)-net in base 27 for arbitrarily large m, but
- m-reduction [i] would yield (90, 4801, 2402)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(274801, 2402, S27, 2, 4711), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 120474 005349 963336 309498 078257 034145 018023 708409 106093 039612 942846 635500 124753 978545 199448 247041 930618 423057 392167 363063 363205 256554 428400 817492 244875 901402 354605 957174 580501 265000 967788 333879 553867 972147 762871 684039 844109 148463 454575 483902 218443 644741 742813 094409 293546 315966 137524 859873 188823 218138 113204 086026 575364 016637 867511 379477 866602 095540 019957 328657 565989 145883 590221 307758 182053 055533 850667 919058 359090 815769 042670 478652 882904 791777 775248 571798 983015 868031 423443 767578 907649 307549 918377 737515 281899 118642 105995 472888 940547 248495 208686 951242 257001 273276 969559 792945 252746 190226 405912 802076 600307 787557 992576 598522 367526 153244 488978 334393 331517 784402 553677 273584 120567 823945 535735 977142 180588 883767 037591 947849 246975 324302 637065 535926 666836 422741 052413 504013 446464 681475 636351 088132 677838 827013 809223 356148 800934 627751 513032 839941 076453 476071 565614 211936 638697 671240 986589 356021 180177 672900 586343 010329 112912 289010 211106 934444 725188 925893 830851 926062 238314 243898 846695 413810 399296 589740 630901 182275 683630 248852 379881 277465 638764 988869 371406 726473 378108 921549 894033 841174 574116 317279 835224 227765 204724 394066 205320 059404 625581 908192 439538 424439 205294 821373 097480 788693 987944 810859 791256 997839 244372 842996 226296 296135 142845 859641 891935 946864 942190 848528 912850 817362 521622 048386 851087 309348 231076 473464 666592 641169 055277 453582 178752 503704 117417 735548 899086 670036 711736 045224 883261 429512 601493 062553 531068 870539 918909 549328 657595 459847 363596 483353 840963 044716 937300 574646 784836 937727 648930 836190 487990 163126 769804 998782 198034 189698 639194 407467 046376 148868 931436 333317 889623 303221 456885 566318 883781 871629 194231 345141 885102 243126 450724 995313 318779 314070 103794 633745 525644 711613 445882 782070 343188 902116 318160 328099 868499 051202 320208 803394 158282 045019 042768 376652 125105 916051 479262 827835 420556 956520 965459 696832 541429 201603 441666 294115 096208 538389 024901 960252 031720 801861 385593 384852 510564 884259 497962 998450 202668 545158 656040 292110 233492 180267 357009 976233 895531 364468 978892 761772 164032 589582 030570 373634 439543 618900 177790 292140 982745 541996 452100 871689 755291 999763 794462 949553 091709 309009 923108 061036 078833 961848 701879 117434 476923 954743 511671 859320 655392 242764 927467 448797 720715 279323 290874 092912 720789 092695 172169 366098 169313 120225 015999 454688 138184 900990 286007 700603 202788 422862 814744 881627 400208 762504 128385 885182 375526 984498 147964 967031 917125 856798 719421 810150 537307 639966 234612 203744 397487 854177 018653 789175 502406 076480 230632 114873 413896 001400 550446 684397 273371 337344 276139 345837 883895 872534 798975 877186 720601 395320 512102 697663 220372 439122 345147 793262 859965 411013 355724 225135 756081 056617 644527 216111 064485 085496 705024 875653 910994 384723 113749 353774 292754 945250 299074 220124 520267 776950 759771 922240 538802 792669 817010 050307 108598 118274 849928 479804 293009 498496 692756 123396 420360 369956 995904 555541 100252 894027 030043 630700 369695 360560 411114 161016 258827 218639 665295 587296 977079 425203 075449 903683 618964 346953 311707 703837 120824 161959 787950 679344 618560 192935 671600 489062 548375 647873 883333 134998 302798 074672 163221 403515 238654 396935 258120 934713 871198 039529 788250 727594 022504 988979 574340 137730 101516 905866 123907 207548 514240 216008 368491 300001 548377 744572 304233 238499 121331 583761 896516 527138 799810 208802 858555 060739 906298 893503 588618 976474 488049 513514 210464 964358 527643 911642 334087 996481 114695 374888 583558 409574 068385 780435 867503 929235 861573 201107 063532 562426 579934 638248 495313 298302 306610 788494 778697 869117 371213 519880 623938 828083 520277 854702 895580 752536 277660 971816 124068 721463 033468 397929 920964 337736 157077 612192 251473 951379 159416 833640 291875 607317 417700 442086 163640 275538 415113 772647 686470 334934 251946 101564 020220 775523 744326 634288 087115 542405 616434 478895 194815 488897 487841 710299 280782 089209 749544 228265 145564 259549 291252 694746 917671 391139 236692 272338 426357 766988 882749 820992 633180 745457 617355 451331 378647 147834 622107 246788 480532 365690 539946 113240 065206 734818 314396 555660 984269 084706 375464 672393 702149 850782 817483 582775 915553 303665 022433 632247 761736 403338 075870 675092 415660 709649 300617 372132 019464 875019 812791 268293 973396 466957 023671 155049 667170 412669 808549 940667 229814 254140 781460 683651 461789 106577 353014 729687 216751 287182 380596 407505 103303 792425 647403 992470 783589 678903 221389 992229 194999 061104 121079 651723 233635 795095 312495 270876 613440 172081 431678 035430 346907 520002 356494 355394 995235 296426 181313 875284 516621 736933 298373 961276 138070 214781 512332 510928 971837 426022 424458 905824 371172 063334 230248 447028 931331 474568 340769 579167 611293 697476 598196 197785 613444 470162 611272 544463 501626 610248 756933 354920 733952 106153 331413 839289 211111 930831 188767 022644 598747 027459 394411 343465 285608 449754 171669 811083 116934 660004 921966 085712 384165 118535 509774 818694 544119 882434 166571 379354 835339 707981 895207 346523 936802 606250 394778 988164 582289 492685 147858 522465 410711 574466 699641 022422 548736 050736 145250 479324 146800 670296 187338 375137 000722 837288 261739 929513 284356 715121 055895 581009 235641 021008 620741 184603 950255 495737 414301 116023 985205 889042 796249 638473 421296 042001 812818 694573 074033 260692 743730 650742 170883 104027 763238 027206 859795 655749 610070 151649 943396 687973 743411 914388 078979 550710 490746 449994 773807 951954 943773 344645 632349 207402 836508 212686 982890 917036 216518 101152 639315 140578 216491 524319 885141 682986 099999 708339 677003 929841 674767 060253 172928 902965 279009 111097 866986 209787 199877 125449 292989 163237 361316 688894 353443 824246 612711 526660 173780 511975 534695 887407 428245 940874 349888 554181 013797 892330 367904 700479 458804 391042 038575 671030 722700 978445 827176 657650 487936 745342 013715 090604 824589 169847 996532 297091 673424 936149 208883 519791 430223 331079 663365 257778 723962 704943 420411 681193 608481 218083 219134 415578 435905 522802 672681 004857 390776 453685 447675 976442 568449 591293 776574 608499 544321 632357 640150 324793 722949 905567 932455 442959 277247 766647 287962 475875 699884 371115 813552 634059 915372 155207 597834 697200 196717 363194 423038 567822 619580 787851 048430 097815 558647 491739 193535 084897 235892 715350 563019 013286 738644 287663 850488 167314 707958 458709 795057 532323 102400 043349 373865 325423 139234 691652 341323 741480 169307 700882 424935 839669 390163 275705 964429 753639 636105 418486 943702 926800 874875 568474 825318 219219 953623 297273 306545 696494 553116 896165 602985 146017 103556 132565 514854 357294 631307 492464 515884 629924 570606 392622 502605 953390 933111 999520 187763 810084 977045 346078 906002 337705 973150 059441 865343 984946 950440 887155 860304 679244 664331 841829 765879 281748 597095 622397 383240 208393 410578 703547 296880 508279 566536 647809 629250 351966 109499 387208 925194 007433 968573 095210 095051 930001 368627 605887 465870 040253 277750 734497 792794 815777 825120 159648 358362 811437 700641 323075 795073 573164 709207 614364 409850 181860 707067 852844 746008 202613 064893 767714 399054 153991 130161 465224 249050 115895 259970 983716 697307 652555 126517 838648 323147 063052 442405 214920 830689 344635 334514 943726 075081 217875 220040 377269 038882 225447 805649 471899 282446 517430 428800 822060 384238 145738 309193 789141 210083 971349 620008 909519 773571 507614 032394 202327 030094 034174 694471 648142 003205 896999 114217 218263 / 1178 > 274801 [i]
- extracting embedded OOA [i] would yield OOA(274801, 2402, S27, 2, 4711), but
- m-reduction [i] would yield (90, 4801, 2402)-net in base 27, but