Best Known (97, s)-Sequences in Base 27
(97, 323)-Sequence over F27 — Constructive and digital
Digital (97, 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
(97, 324)-Sequence over F27 — Digital
Digital (97, 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
(97, 2583)-Sequence in Base 27 — Upper bound on s
There is no (97, 2584)-sequence in base 27, because
- net from sequence [i] would yield (97, m, 2585)-net in base 27 for arbitrarily large m, but
- m-reduction [i] would yield (97, 5167, 2585)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(275167, 2585, S27, 2, 5070), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 3 687115 774860 629477 375786 792570 429164 207056 165800 325378 627427 192091 590375 081999 216443 326814 923767 868471 847655 475694 416250 695357 980394 184690 041821 807483 824219 649683 690975 688290 183565 895474 549448 190371 855582 489086 841663 321774 706574 390936 948910 135034 123277 938407 064778 955154 233385 737551 927574 630900 861931 946856 512695 491379 837296 129364 023686 137198 546864 131271 270048 732790 010232 167393 836761 105247 096210 408712 827687 709369 554562 447217 496215 723874 350212 948220 524065 011320 098395 039860 958324 815793 603568 256080 523480 881458 927094 367431 682028 651828 816112 906267 115062 853987 693582 538664 359311 874831 335415 962280 143666 724510 964623 633276 956367 231443 338949 478025 518849 446203 379357 543463 110746 442918 100317 938773 923574 900805 800502 470517 597212 502033 868903 426788 866330 925202 355831 632214 601867 381915 450758 900561 982698 711952 766054 336946 267208 354529 803800 382185 582635 879329 004221 257858 251993 620592 900147 376143 292357 917453 639070 548017 554293 217751 939523 795789 326799 773917 824644 016059 476629 158329 135624 965974 594238 763348 559591 243846 914151 805826 980110 458480 030839 288546 027426 150664 128661 572591 323333 626136 304689 123575 682017 868319 460553 390753 100537 614977 446853 175371 381943 526304 145626 631068 498164 184254 110460 722094 605545 926175 793592 766684 828560 250350 352757 724876 967871 694033 862764 349575 830433 775336 020305 668603 167905 513251 503269 010849 368182 095362 881377 273300 950725 046746 597004 947152 326167 807969 123070 302291 467406 406772 327187 228329 346151 148602 042242 513417 613951 924759 490133 048888 360409 449322 114416 554384 708169 316131 972393 766489 547651 806712 300761 809158 447723 657498 382922 827861 205206 374303 640040 825136 432921 743093 084870 727830 773515 737531 330003 025276 865429 823390 541300 337474 053491 531897 730179 267720 558511 382602 826089 366787 982980 654595 487748 358866 766490 195424 213854 052645 869885 065431 062032 286195 870658 459928 588919 408241 896469 158418 499939 917905 531924 161151 063542 891628 876220 666824 016475 382247 735456 802880 045617 663942 443680 676219 982029 033900 907700 725355 583571 831294 456447 177045 180143 038842 437677 019979 181261 320679 119554 840810 480909 051582 658249 606298 688645 209654 638972 327696 534940 074836 503821 272946 429055 406564 370526 778168 752705 246398 344568 898227 103542 576509 818821 601677 149686 388863 883430 061663 072820 489468 146923 434277 249563 186500 108649 917953 601596 323360 414411 356703 102774 785852 989992 681613 816100 206471 811032 755652 418882 371971 090058 668972 298272 713719 634580 990925 729106 898807 710326 823430 562828 222950 650600 516957 133230 080127 096302 235234 802599 712359 820100 972843 162165 288456 170758 653770 859382 841851 436906 489105 006738 908221 121447 050547 457978 741107 977807 601047 000498 643343 773103 335159 004293 633232 279184 187888 969196 044483 091897 857085 882525 575851 715149 103418 501364 882125 381894 625161 651500 567746 177444 923549 132045 289828 135486 606778 875373 568689 160418 924047 155402 698772 061355 165647 392173 406908 362324 023912 619580 472225 732747 320095 480808 370383 522305 175292 680499 991002 186977 361864 756758 389686 640396 176750 160477 377696 436954 096017 877599 922593 733359 476504 039740 896170 950270 298259 820665 492753 932130 471058 143320 894089 129344 801339 671353 890170 140186 109711 944841 021687 097157 274062 603378 730526 887629 277634 571880 951389 375249 427711 339031 304759 853744 189770 776471 779710 770737 883180 551583 815614 605167 127720 806731 819483 712486 979533 235814 481578 991700 930543 823301 857519 674838 447041 727461 525950 987496 893496 889425 497433 526620 765446 448311 493717 354997 995189 377333 970499 639078 103217 127230 770684 877252 600397 364147 449405 266647 515903 736772 056266 324622 920811 039414 926145 730233 455996 436368 713887 312566 899896 546462 568928 684378 607918 843448 595602 378862 392152 265672 417596 433265 090784 700664 751182 625496 874505 569617 208977 894038 410077 683259 487008 278637 171261 249065 126337 008798 628711 862314 755061 708609 375390 442011 150500 515351 848699 207046 192579 653001 702073 647707 082449 822728 451077 595900 811100 481259 603541 747241 599290 889992 369864 751248 485761 231235 792149 616096 274293 655880 062438 787096 528507 512326 332779 044815 859394 226132 900328 245188 599657 614641 647229 929884 757928 966969 624041 206172 370864 987845 869486 923621 655746 389393 755466 835470 795802 642263 889965 092943 896646 247914 243789 020081 220383 912838 499663 248980 279843 752841 390247 996295 214773 369978 889878 282577 760589 840021 581645 525060 647558 690149 397077 059995 747910 434051 865104 720377 601791 048860 928350 260778 206428 408457 021247 331655 797825 035199 216023 016563 029253 443528 579973 026223 885928 673146 327703 186414 957280 869236 674887 971984 650356 439468 534791 307206 582262 236900 925266 717747 687284 272207 594581 442988 097628 897900 034960 929283 370910 460581 772820 548021 896720 784248 793847 531749 212295 140013 286834 123471 067865 495930 613063 654823 539566 035493 609673 927524 748247 881196 905833 047025 819541 206514 762662 058947 830722 425851 661626 750118 148249 660421 393614 331051 962343 951689 648710 017882 820277 720173 586311 726180 262910 388253 561326 654280 016176 911395 051025 156098 635914 856478 939572 612903 453067 869100 283232 180857 112122 247214 207953 015123 256725 385227 222380 769390 087331 801102 363864 006357 594137 024507 849452 808915 099812 902855 818440 822265 546289 872182 823940 029497 461668 140777 267693 658998 794327 104495 156651 757190 864684 346335 276113 430764 392869 860207 623888 414750 275975 729775 947739 096585 769924 481105 771312 068183 864052 117817 018905 814918 501190 774756 988358 900526 092246 872307 124422 069338 742767 173618 490717 436321 500836 756584 889634 233433 116961 764110 207786 546433 808402 673088 626943 718638 030033 356841 340948 839260 457710 286802 628450 808841 544260 908083 971247 853476 720961 451751 648569 575906 558050 790205 293713 195433 964403 335304 688588 082934 329600 554351 984658 266705 997234 345504 128776 557734 817797 626498 602037 579096 404506 022221 167622 540446 326333 742385 865564 032964 053804 240214 118445 166312 993883 332914 901718 251851 399607 989768 049143 443827 432290 612619 166381 085869 690149 307376 061686 925188 903554 899589 552870 602379 202252 893200 352248 775652 107120 826849 191945 919854 438594 015830 030637 368132 876108 847876 626382 764494 075885 374546 436749 642493 199545 042824 678890 292837 005950 946236 485519 938930 771047 510917 105618 527853 460990 134251 456195 734436 882584 046672 411200 152358 158054 167048 772524 870025 654392 712481 742549 474569 021076 259536 960908 086620 269531 831930 043378 560998 555313 231182 953777 588774 092526 229031 108671 278737 009742 868489 597955 595772 740871 588257 777072 312849 637927 309064 926531 385465 358058 967206 998761 247404 170161 315854 223116 025168 298305 089859 148282 586741 018614 070456 567129 802930 740470 961821 028526 375034 633597 996090 355783 977916 782849 909211 684502 625270 902242 644815 202836 704967 375777 280419 315487 379396 128561 947623 422688 631819 137237 125979 406321 939287 277554 649674 847895 314482 616417 681307 022378 691541 148198 585149 594447 395987 030976 572587 431768 868671 314673 692023 842110 797811 548100 066261 524291 447697 070889 148678 540430 279964 442985 434469 812351 136996 780591 153068 120151 773315 767384 379525 778923 414348 877796 426991 156472 794353 914973 156697 974096 825076 146890 308304 081971 077994 015804 783621 614460 157150 382731 909487 909890 536317 106325 355928 789716 582234 750475 879301 805814 435547 156108 839109 335768 992975 492068 256538 174127 385698 792854 042533 969226 306957 293182 315854 896798 003030 409694 251228 099703 892822 429165 239108 749395 778767 551635 971431 299383 462325 826001 778014 633170 613828 118552 756970 979714 911185 779074 801883 698425 551120 562308 153251 963996 015660 350886 418547 453566 658988 389929 980791 582309 665131 799690 701480 147164 414928 976174 797653 495212 594149 124206 014870 620290 715471 975000 471401 417076 602055 006756 983703 129396 775900 940480 900197 567215 201386 350714 484851 601300 776355 537624 515607 196333 430625 209774 872856 531370 192264 401503 103778 084927 598133 338080 479467 549816 414980 819748 342206 051226 951117 667333 694842 778097 229720 802448 132847 296081 461992 655489 891537 720567 353895 491539 / 461 > 275167 [i]
- extracting embedded OOA [i] would yield OOA(275167, 2585, S27, 2, 5070), but
- m-reduction [i] would yield (97, 5167, 2585)-net in base 27, but