Best Known (84, 84+∞, s)-Nets in Base 9
(84, 84+∞, 222)-Net over F9 — Constructive and digital
Digital (84, m, 222)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (84, 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
(84, 84+∞, 245)-Net over F9 — Digital
Digital (84, m, 245)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (84, 244)-sequence over F9, using
- t-expansion [i] based on digital (81, 244)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 81 and N(F) ≥ 245, using
- t-expansion [i] based on digital (81, 244)-sequence over F9, using
(84, 84+∞, 699)-Net in Base 9 — Upper bound on s
There is no (84, m, 700)-net in base 9 for arbitrarily large m, because
- m-reduction [i] would yield (84, 2096, 700)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(92096, 700, S9, 3, 2012), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 102778 152949 177063 824089 374579 989528 213736 853694 337848 222186 630723 486911 348966 443655 140469 435177 085952 240619 855522 582786 691001 946082 799554 886784 679612 673993 032430 666554 820920 592207 251092 970682 794533 574366 476494 797621 651687 213712 898157 175715 936726 305991 738588 188921 606700 708674 033943 660679 951790 223817 524341 498286 693801 561253 158049 959546 804297 094270 011300 928650 649360 701313 874287 397859 227917 521265 270235 608503 308053 059033 496031 138037 492423 637531 394990 644968 900144 432194 716418 538666 465384 188473 975228 797775 204909 944139 538389 466691 774612 069401 399309 643424 031225 332086 773660 428598 250004 632485 738748 930384 935304 535540 483810 062710 251692 026112 766493 061635 249451 149107 907528 225293 041600 223760 653454 427940 916259 518542 605643 928473 104578 517761 542105 884110 938847 617208 603276 062215 735115 171691 152356 033152 867427 690512 248615 151614 557668 883582 528467 901738 663670 139723 435868 593300 920148 143320 056111 338527 309765 676923 123613 876577 867266 512254 364224 430727 224816 792927 579071 294190 845007 463226 928928 645027 324472 825770 683527 913889 175509 309995 204330 639675 380977 711604 306062 786174 681210 695504 582738 977015 148043 099139 022807 024685 632334 037415 633681 565454 744051 613323 637670 032897 649864 590212 150857 599202 784706 747031 130143 368939 496151 066140 435248 773119 506099 402067 525615 492869 538843 165968 157369 823358 028393 393653 187124 098484 042192 418097 812681 303921 403773 939698 319117 654810 748827 419487 504633 383887 013994 363924 460137 695827 917966 760351 391766 113328 638847 730822 081625 303668 564640 245698 906588 089932 751719 840783 463237 461281 793841 499832 308511 075591 791828 857418 938411 984314 717191 941632 624678 609628 823161 074643 453739 662065 043412 566823 899917 152252 734675 870658 429935 110756 573464 294091 607533 656647 608286 225717 455119 137575 554203 830432 585519 114457 013389 480499 835759 233572 629290 486149 977637 489084 049205 327565 141055 148603 144215 492470 346100 324270 973956 233233 477865 559923 759258 685520 995106 530947 516396 653437 173811 802417 688883 270741 671075 255582 730099 034353 383419 592543 307553 602294 207961 916478 443369 144166 103975 633560 276380 505281 518466 344479 144440 539071 / 671 > 92096 [i]
- extracting embedded OOA [i] would yield OOA(92096, 700, S9, 3, 2012), but