Best Known (241, 241+∞, s)-Nets in Base 3
(241, 241+∞, 114)-Net over F3 — Constructive and digital
Digital (241, m, 114)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (241, 113)-sequence over F3, using
- base reduction for sequences [i] based on digital (64, 113)-sequence over F9, using
- s-reduction 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
- s-reduction based on digital (64, 164)-sequence over F9, using
- base reduction for sequences [i] based on digital (64, 113)-sequence over F9, using
(241, 241+∞, 163)-Net over F3 — Digital
Digital (241, m, 163)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (241, 162)-sequence over F3, using
- t-expansion [i] based on digital (151, 162)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 151 and N(F) ≥ 163, using
- t-expansion [i] based on digital (151, 162)-sequence over F3, using
(241, 241+∞, 497)-Net in Base 3 — Upper bound on s
There is no (241, m, 498)-net in base 3 for arbitrarily large m, because
- m-reduction [i] would yield (241, 2980, 498)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(32980, 498, S3, 6, 2739), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 143 150482 355324 843298 710064 733917 540214 656130 139546 676119 906425 288897 029313 694895 807230 482725 425236 421291 474907 861058 018095 176261 233781 244865 321340 480187 298607 959056 006028 820061 093656 404475 731800 635603 062644 319348 812429 350477 912786 564492 163482 170577 598990 737703 092087 104139 403721 129806 580614 653251 474009 657582 475573 024148 749447 341699 701715 026152 692642 496622 126246 549814 479666 733899 650824 865417 762873 985070 037903 433648 426752 167060 068753 365949 206673 084128 562179 216215 168958 007238 129553 018118 186855 364422 169433 236228 930773 786040 200389 031266 926237 020652 125715 905126 170365 897048 638574 588262 431720 909020 490950 088075 097141 172840 060575 214452 483848 532310 880967 375976 848818 862124 371442 826076 785847 958048 140224 233486 711317 245877 795623 973505 744228 451383 826860 464416 006623 523075 354787 363417 941290 419852 283888 516458 706471 372646 585423 423825 228625 587925 124383 429504 004973 929929 342299 855214 858598 743273 776764 321074 651721 241789 070874 735406 759089 731898 725693 670640 418673 681100 877528 802809 016937 523345 265880 697763 457984 912742 487191 651941 268964 104003 389727 232927 353537 886048 788957 066423 492589 621443 551935 028817 454044 149615 561871 077843 355141 705475 218424 748380 173685 511998 395503 822436 548221 338792 050022 268407 065712 616993 123708 535024 424676 842011 847165 023198 824091 739965 515249 285395 405578 728180 751423 826644 099854 595545 457675 233604 145191 394275 200690 322778 494272 319265 722716 679494 337545 882970 297526 591465 312338 200394 690721 669293 571133 658501 067234 889816 / 137 > 32980 [i]
- extracting embedded OOA [i] would yield OOA(32980, 498, S3, 6, 2739), but