Best Known (5, 5+∞, s)-Nets in Base 81
(5, 5+∞, 160)-Net over F81 — Constructive and digital
Digital (5, m, 160)-net over F81 for arbitrarily large m, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 160, using
(5, 5+∞, 167)-Net over F81 — Digital
Digital (5, m, 167)-net over F81 for arbitrarily large m, using
- net from sequence [i] based on digital (5, 166)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 167, using
(5, 5+∞, 492)-Net in Base 81 — Upper bound on s
There is no (5, m, 493)-net in base 81 for arbitrarily large m, because
- m-reduction [i] would yield (5, 491, 493)-net in base 81, but
- extracting embedded OOA [i] would yield OA(81491, 493, S81, 486), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 6602 787619 728855 354943 588158 976993 785872 513143 119027 992120 051397 324154 334169 036842 067863 524252 568394 126114 367757 893821 163349 111087 784916 455789 368008 784693 466674 322381 038472 962543 089979 796040 599399 986126 075085 905536 798705 747900 550251 155816 390914 080827 901696 266984 413905 959728 125268 614671 953206 220122 478517 748324 264128 929304 123658 625807 602814 885401 305797 030076 558339 914423 104644 567096 983775 753589 188696 725706 144479 389386 891250 007528 142200 085470 622573 348274 916541 861251 877644 394303 198138 817154 483850 088650 250211 208561 112679 923351 584897 981704 412832 517511 926898 036040 300550 226931 610520 518461 027948 464484 515821 206063 465489 088322 545532 804894 966755 493204 955411 187888 844182 984090 338828 133056 695486 374142 256907 527487 050702 357819 168707 791843 929618 974667 927714 609435 761972 813357 491079 970844 803494 439490 425774 086525 016129 174616 136667 528418 771721 454463 052321 914739 910863 915169 781482 326637 102719 050873 843515 478529 063531 474588 643352 782510 301985 539291 808327 / 487 > 81491 [i]
- extracting embedded OOA [i] would yield OA(81491, 493, S81, 486), but