Best Known (97, ∞, s)-Nets in Base 9
(97, ∞, 222)-Net over F9 — Constructive and digital
Digital (97, m, 222)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (97, 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
- t-expansion [i] based on digital (79, 221)-sequence over F9, using
(97, ∞, 272)-Net over F9 — Digital
Digital (97, m, 272)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (97, 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
- t-expansion [i] based on digital (95, 271)-sequence over F9, using
(97, ∞, 803)-Net in Base 9 — Upper bound on s
There is no (97, m, 804)-net in base 9 for arbitrarily large m, because
- m-reduction [i] would yield (97, 2408, 804)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(92408, 804, S9, 3, 2311), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 194 410259 162203 166012 726337 092180 061940 575655 862387 875712 878283 210319 066967 458241 970721 179146 589112 303796 403209 611712 759086 421668 278231 487369 393785 662595 799916 463091 796447 304906 482145 890445 161271 600105 260962 769737 819304 330321 095802 873777 022315 474210 457902 018092 311530 822166 289815 720907 584009 548448 979117 800722 065854 613013 693652 618108 679075 390760 189400 369079 182126 986033 177257 474835 554762 801504 437718 387860 745990 506923 755513 509320 051198 848258 033498 700604 701845 813655 616204 348940 119669 615160 038540 550293 826130 052748 586074 894897 768537 420951 264847 395520 755421 890933 612376 656117 539017 032699 819207 376949 059101 908296 625590 281243 939431 477731 670596 540204 895731 449550 351243 330255 557972 796274 355249 334249 778815 945033 425595 096426 739046 832282 576698 248328 306179 721950 920845 575306 581573 456302 685490 748382 534311 237383 558591 067188 474781 317358 143935 290801 887266 164946 189525 264905 347879 303146 388911 383963 057640 291951 009325 403931 217643 930315 577350 415845 560775 526542 898647 237528 824342 900994 720677 982106 252386 211963 480768 186707 383612 042359 645134 970084 356860 600783 984999 472115 010899 410645 105434 555376 923266 345891 831194 859167 365690 842704 797693 400332 837519 968576 938901 583315 613245 625684 238412 289523 957392 554065 151282 408746 249566 772983 781371 961937 666632 576562 676204 552120 717382 789255 990106 770283 019722 330144 106098 237564 654990 714689 991600 472527 013732 250140 197403 481948 813413 163960 289983 149470 048757 166498 912120 576608 233126 159916 387349 733825 711873 846946 585252 626654 264057 210264 309989 533430 404559 589472 079209 372965 180786 415991 670439 990817 046008 114053 661348 931548 638959 030090 280145 880070 258414 696381 880844 729301 371805 580900 355808 272981 371251 365763 931862 001799 788165 046425 667261 065835 199464 326438 652130 975661 330869 837699 868750 171664 473230 019552 490378 091921 685758 721986 883123 572145 499746 311081 604072 339082 867099 435040 724002 991995 284202 286222 670099 895865 430081 988509 120380 869875 160486 523591 016019 511985 770677 634060 290591 332515 893755 337694 160873 686530 719730 507579 279079 517426 258824 345904 484334 160013 461764 145048 687963 585268 672648 873324 994711 870016 150778 265342 489691 717537 991790 045221 989895 809799 350171 791028 471553 532114 065665 050619 574110 016087 714881 560577 398454 241905 259410 681258 789680 607995 358870 666699 102295 369982 611076 711646 182741 559509 064751 124454 365751 598996 702165 923270 218246 103004 420446 734713 121532 136281 194471 220393 784329 548137 / 289 > 92408 [i]
- extracting embedded OOA [i] would yield OOA(92408, 804, S9, 3, 2311), but