Best Known (99, 99+∞, s)-Nets in Base 9
(99, 99+∞, 222)-Net over F9 — Constructive and digital
Digital (99, m, 222)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (99, 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
(99, 99+∞, 272)-Net over F9 — Digital
Digital (99, m, 272)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (99, 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
(99, 99+∞, 820)-Net in Base 9 — Upper bound on s
There is no (99, m, 821)-net in base 9 for arbitrarily large m, because
- m-reduction [i] would yield (99, 2459, 821)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(92459, 821, S9, 3, 2360), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 3215 338282 934097 498029 634203 104373 670321 027573 677758 961930 215497 606842 654556 085832 312562 629105 262527 650391 947713 303173 761691 825808 475166 168035 711584 575253 280417 663153 956110 500790 423850 434493 462355 888935 403401 488438 960399 840341 325030 924812 538588 276298 530917 810200 111694 523334 116525 185629 902321 122333 870689 592005 643309 318593 468522 804880 915546 229872 331608 432303 083204 600427 087316 344924 593194 159523 425451 368624 588362 855921 994712 972267 921996 237163 588132 364011 917337 621768 298523 380771 472967 675706 840993 002156 818179 330712 597465 751781 610981 296019 849324 237127 058374 275660 353849 944500 802386 360238 468480 880883 269357 480835 167698 512837 236531 457788 933695 157863 506304 676320 821681 019539 002036 969621 960487 053080 822508 489029 350422 593211 433274 467246 913235 715146 530254 420987 573501 704798 806397 328333 187920 184741 076835 403433 137382 310577 411676 860656 626255 352324 736145 845465 601502 495531 786847 888274 248549 963055 831803 454482 190562 946586 248998 003790 849455 657744 864232 091360 365027 345532 279443 075671 331141 857643 000405 124913 043391 816164 522491 229579 410477 473513 149706 602920 902616 624346 869358 168263 534914 400237 951150 425457 391217 772847 631847 455692 090623 630836 670992 599026 357627 642994 234507 097461 995537 989772 015458 576975 391127 036916 061719 200743 634639 005061 488255 632893 328702 392776 480816 422224 104438 683822 220287 846931 854700 980550 518824 894380 580757 594150 684217 224515 550967 812248 978142 488490 848300 706706 857275 296393 103102 759858 714310 961977 668219 534225 111534 253195 929573 959662 320198 320563 539758 385040 324784 302631 187166 861226 221959 070819 867638 504049 289659 879113 864630 131007 951628 236293 568272 050616 435904 032611 372692 333899 361663 692976 541547 551586 934753 000032 594442 163783 213090 843386 177545 890157 419326 241380 348756 582318 711390 103945 056931 379523 923607 468454 797337 785710 236326 386177 927555 183649 391000 740541 222735 566460 217737 303971 208414 083234 677316 976501 938749 640745 597434 373989 447572 231751 486149 014962 831065 318482 466102 458124 612146 033035 880581 454633 278484 622110 316202 462953 579377 748026 226434 006172 925849 640532 799329 661961 025321 543894 019638 353281 808276 370068 109888 169626 121119 096259 287271 557126 942754 815804 597624 863948 995795 833539 946242 474468 247327 280063 758979 874932 745555 896492 767757 366901 123277 634150 873529 602676 076612 233120 001680 747824 984054 713221 785270 489325 394900 495399 298386 900315 462075 137247 474735 326394 214755 214631 725627 918670 295256 236377 982406 063289 709174 832332 255039 352951 499088 175851 / 787 > 92459 [i]
- extracting embedded OOA [i] would yield OOA(92459, 821, S9, 3, 2360), but