Best Known (65, 65+∞, s)-Nets in Base 9
(65, 65+∞, 165)-Net over F9 — Constructive and digital
Digital (65, m, 165)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (65, 164)-sequence over F9, using
- t-expansion [i] based on digital (64, 164)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 64 and N(F) ≥ 165, using
- T4 from the second 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) = 64 and N(F) ≥ 165, using
- t-expansion [i] based on digital (64, 164)-sequence over F9, using
(65, 65+∞, 192)-Net over F9 — Digital
Digital (65, m, 192)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (65, 191)-sequence over F9, using
- t-expansion [i] based on digital (61, 191)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 61 and N(F) ≥ 192, using
- t-expansion [i] based on digital (61, 191)-sequence over F9, using
(65, 65+∞, 546)-Net in Base 9 — Upper bound on s
There is no (65, m, 547)-net in base 9 for arbitrarily large m, because
- m-reduction [i] would yield (65, 1637, 547)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(91637, 547, S9, 3, 1572), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 229606 576234 682727 462066 090003 604810 376788 554231 627171 312162 301613 765344 506550 671272 946984 908981 494942 625337 293048 713408 817139 321731 604968 390342 347396 231844 405362 441303 562767 783117 683982 386743 773806 848233 850939 156355 203623 605794 498477 937047 873482 146858 123850 651737 344344 120459 797225 706474 225871 840071 474632 878722 831987 850025 798015 308931 879345 216391 912258 839262 730510 751220 773585 607325 322125 637569 085837 963904 188257 376562 583388 538726 344935 244441 958382 515730 289012 146736 852689 343157 903109 957024 564967 070213 936453 486237 351378 852023 340557 920553 262638 452037 985632 688618 826039 195458 686527 667770 125278 116221 782363 898155 745465 987887 001851 261981 902430 530340 193702 544310 545816 622818 916015 125347 568360 070079 857493 009300 985741 509435 403422 171864 519255 982264 718349 071922 558495 073335 726970 664301 360261 311792 306597 979086 203749 456247 011220 570076 063578 368056 155776 372148 450254 626986 558126 603561 587466 468319 362771 926604 926825 292165 593785 933865 270737 545453 483501 840435 131312 494631 471265 029653 923438 281624 799740 959927 797058 217623 312913 163728 510382 871088 770220 931649 182013 557412 334940 816993 418885 343507 125994 608486 170703 853856 818467 021459 165647 711329 548366 899477 480200 613802 846207 096053 770076 451664 676247 989321 014008 977818 688047 939106 374972 737000 059605 190387 637485 360234 341995 461547 864975 895821 461300 889095 944949 980221 784390 048436 922969 275492 937306 586873 077715 628028 073511 842768 895071 048068 035386 489410 818406 600688 668213 385912 898978 015595 356667 824201 499356 810902 769413 864180 744453 571032 634198 956205 149464 801049 159772 476770 372112 611224 855446 463441 827367 870223 995606 794113 034537 304798 423805 / 1573 > 91637 [i]
- extracting embedded OOA [i] would yield OOA(91637, 547, S9, 3, 1572), but