Best Known (26, s)-Sequences in Base 81
(26, 369)-Sequence over F81 — Constructive and digital
Digital (26, 369)-sequence over F81, using
- t-expansion [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
(26, 499)-Sequence over F81 — Digital
Digital (26, 499)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 26 and N(F) ≥ 500, using
(26, 2213)-Sequence in Base 81 — Upper bound on s
There is no (26, 2214)-sequence in base 81, because
- net from sequence [i] would yield (26, m, 2215)-net in base 81 for arbitrarily large m, but
- m-reduction [i] would yield (26, 2213, 2215)-net in base 81, but
- extracting embedded OOA [i] would yield OA(812213, 2215, S81, 2187), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 170 188353 756549 666655 870128 673982 702885 659177 399639 225673 977317 463653 311741 963177 500855 280080 459023 979717 329943 388961 761419 449427 929235 178863 747081 707745 170892 370885 262332 258598 660336 872225 033231 146228 340817 441458 471245 036921 351026 503841 729857 709945 939435 681554 031918 977782 461303 738295 002271 276471 526858 891756 098792 601582 730036 902444 709435 766725 728187 807102 861255 315830 473483 490792 959462 896309 411655 286728 878609 002062 600289 055733 767579 839030 707493 040048 112804 723683 423240 983780 557407 238803 622274 803743 361182 456921 826954 925241 586116 130186 423698 549957 283055 451507 298693 063460 728036 938992 584325 773489 058003 689286 751450 013927 231463 397646 074408 277414 175683 880145 692082 963021 846151 277106 900571 073600 812566 100002 379138 529697 288381 195136 642941 855645 655240 457831 679367 296950 884831 407674 779605 392523 121448 777682 390744 580499 872632 227596 525756 723355 244112 486536 148878 487158 187087 212026 898333 306828 246305 401734 864074 159639 872539 942175 475252 708767 838398 064556 072377 356495 995803 160165 514102 197904 100750 176713 460982 017167 369712 842971 314303 118161 974345 920636 948532 882707 676688 951129 574363 744115 412330 056129 602743 451112 133541 197084 809667 498779 388376 741090 593168 376621 223413 261917 810003 099833 564062 106270 560799 921402 013340 618285 780444 773199 552139 820049 502018 049541 167097 959905 938268 471850 868478 544437 166449 021178 228430 382951 049824 533535 344381 739137 915727 215569 979645 089831 735551 162001 478743 819892 851258 822353 163048 233152 768560 804681 957129 470258 944580 945556 620320 425034 870472 961333 351454 119764 042043 668358 478957 705410 173185 307382 027058 955206 456352 546823 055432 497674 967819 447023 547846 403229 340957 084817 521806 341709 691476 433973 017419 609816 132242 105390 546690 242390 685165 557904 083640 405722 208756 167668 615100 966877 671309 225036 957593 476127 513516 686413 384820 572355 620053 772519 517224 752970 781637 342486 108642 472764 773470 854656 810981 296402 096825 490402 679497 553699 886010 409314 273315 660672 203050 894474 252723 268730 252244 810496 012015 325461 557787 145000 832454 974206 179271 429503 615954 600535 730252 274803 370610 217044 428558 386793 408646 003296 569272 112240 017159 290466 782080 353981 466400 609003 772970 049494 828577 941715 880079 207503 673869 303182 246906 870684 284611 033266 309715 159783 976906 278818 391158 021305 846446 294751 816059 118974 247196 156293 219050 239528 508786 868280 478044 568826 074300 102963 948629 888796 170526 511026 992016 204822 888095 764884 804693 375978 235954 343417 515097 407797 196001 150270 862999 583781 101405 051955 885220 225144 825312 066647 569478 779466 855084 414009 690050 555693 411497 156103 851677 679781 270022 828205 484010 562910 422457 090161 734876 232769 216207 725181 515318 313108 965949 880623 784837 371516 290153 060939 018702 713370 483945 759848 649288 326337 874811 953465 576893 328901 623543 970953 253765 429692 237633 332997 931129 418879 875320 060237 847435 241756 548547 768692 746168 626047 447415 143107 349101 938340 840956 280972 267824 552218 638440 176352 106041 102567 240675 343195 925816 234411 705482 720379 354021 975589 401792 740193 305034 954511 693436 723913 163161 813747 238966 229268 597115 221043 364448 970120 823438 597226 210667 658713 012881 607076 013433 898915 489760 227021 852297 031693 010542 224174 779293 310789 573473 607246 020672 986594 440375 934325 029094 660427 337312 360274 649209 570815 869659 681865 707306 027580 288633 998162 920886 011122 778213 678586 468847 366046 689623 869188 622672 428618 609441 656721 655656 314785 681638 216557 883377 362334 760345 079382 817423 765560 956973 813495 336438 544152 203744 184397 399493 040614 129250 239239 373233 002346 584692 813034 953371 192212 131171 294144 385765 331451 542732 295823 012384 746397 603626 575240 510103 575035 776747 516849 532462 414502 975290 656654 194495 461905 652270 570405 139215 326468 270832 893990 065056 368032 739112 940357 122361 691709 671214 338992 126617 868009 203866 392537 805353 694382 287945 388374 885811 064883 208500 890783 198452 427383 048389 339050 490927 037870 548074 923553 260463 751357 592404 132119 343615 132627 620042 297868 855697 121447 889557 048306 199073 222149 312067 293896 988613 444250 930683 096194 192501 877610 140634 807329 819101 122721 198754 127962 977710 921089 090802 845388 548220 403176 930792 621045 938937 222997 294994 588127 402570 040156 456115 090236 513259 814769 655462 876662 738638 329445 615031 038514 979726 357060 462158 144166 644573 492562 287748 743834 749816 404073 323902 721959 769739 408250 735438 964916 835322 817890 073534 737033 243479 489417 920664 926204 649340 961008 521329 463878 717885 222225 994154 480562 879120 468450 998657 361702 616717 612765 103044 247791 172647 / 547 > 812213 [i]
- extracting embedded OOA [i] would yield OA(812213, 2215, S81, 2187), but
- m-reduction [i] would yield (26, 2213, 2215)-net in base 81, but