Best Known (100, s)-Sequences in Base 9
(100, 221)-Sequence over F9 — Constructive and digital
Digital (100, 221)-sequence over F9, using
- t-expansion [i] based on digital (79, 221)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 79 and N(F) ≥ 222, using
- F4 from the tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 79 and N(F) ≥ 222, using
(100, 271)-Sequence over F9 — Digital
Digital (100, 271)-sequence over F9, using
- t-expansion [i] based on digital (95, 271)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 95 and N(F) ≥ 272, using
(100, 827)-Sequence in Base 9 — Upper bound on s
There is no (100, 828)-sequence in base 9, because
- net from sequence [i] would yield (100, m, 829)-net in base 9 for arbitrarily large m, but
- m-reduction [i] would yield (100, 2483, 829)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(92483, 829, S9, 3, 2383), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 47 953038 175139 975043 417920 676734 526843 421925 842636 369332 018202 002327 436792 029702 297367 310805 324481 159585 458041 074175 733912 155062 348168 680237 291571 339161 134281 403685 171823 017150 433054 518927 123006 961961 967979 131231 871066 141331 356804 463046 552099 427880 100978 713518 822514 167651 097643 197083 713139 285779 956294 600726 488188 399748 570271 519082 408833 992914 678122 518966 428349 730903 442806 379927 338949 225701 962216 413099 851450 526320 576273 766095 729886 721703 742286 716451 916461 454527 890344 008331 802522 969673 299153 878426 957839 218109 413088 628564 432173 917343 011401 422095 602525 793896 724233 595198 348419 539836 913506 676147 907505 276528 666114 250502 533987 073523 238108 147968 809502 946196 241909 713116 052668 136146 516052 126069 739439 984878 470634 075318 463295 381491 766867 404410 183945 560758 848533 198707 866724 163336 562888 666025 497506 658914 756913 701986 004892 212188 050084 698168 195146 899451 157144 635343 856341 498680 123914 148304 797733 316991 046878 807727 745688 952793 172332 231270 558941 110432 277124 133878 929412 018807 247987 542569 851309 767651 207133 661049 914922 394730 109907 225617 566209 310381 335425 577698 508089 763974 573353 674930 869558 647121 917306 885825 546363 741776 767133 565474 517751 507099 267689 322718 623773 411804 475906 884664 144744 901956 149052 059165 284525 895937 268512 015136 241551 391629 937174 848098 399147 178366 550364 152710 306059 824169 792817 541759 833600 284581 523993 142444 187049 358411 581272 387976 172744 256581 370422 052197 126657 513729 990717 974073 498817 610479 278009 182978 059296 307969 387273 097332 463492 667452 826316 364879 422893 843033 766531 571811 400814 931095 045035 902770 406985 405396 404161 999061 593122 234333 350864 816401 744459 940554 831825 722788 534781 139182 945522 400623 828383 799498 969311 361784 474149 892889 445497 833166 782591 671678 728369 993850 117477 213657 916566 001668 552859 399050 660147 069204 694024 023416 723107 940001 285960 297635 311608 164955 959285 893597 689293 852894 446896 751957 438195 745582 895554 373138 843811 183917 163298 707030 617867 911827 737333 551836 633647 863505 786303 719625 023991 011486 083508 204692 745326 453180 558928 587791 738193 658002 604491 786851 614239 397861 845326 291328 545452 771711 113652 304521 215648 107099 488900 369119 065820 178010 580642 495866 585113 222801 731834 545069 292703 767720 761590 086362 405149 927367 072020 659015 816967 712040 924725 919000 820224 966919 636683 667461 414587 748876 741494 450010 337193 120030 891683 830774 952546 247638 659359 119169 200550 599392 683898 002128 616812 752116 392110 321603 870984 510946 378449 262245 730942 097307 911360 327418 849533 974742 / 149 > 92483 [i]
- extracting embedded OOA [i] would yield OOA(92483, 829, S9, 3, 2383), but
- m-reduction [i] would yield (100, 2483, 829)-net in base 9, but