MinT - Best Known (98, 98+∞, s)-Nets in Base 3

Best Known (98, 98+∞, s)-Nets in Base 3

Digital (98, m, 65)-net over F₃ for arbitrarily large m, using

net from sequence [i] based on digital (98, 64)-sequence over F₃, using
- base reduction for sequences [i] based on digital (17, 64)-sequence over F₉, using
  - s-reduction based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

Digital (98, m, 96)-net over F₃ for arbitrarily large m, using

There is no (98, m, 210)-net in base 3 for arbitrarily large m, because

m-reduction [i] would yield (98, 1043, 210)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3¹⁰⁴³, 210, S₃, 5, 945), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 269 500932 845703 216560 146455 052285 569048 722959 875140 047572 933727 928010 784085 458459 078494 227989 495465 933401 594383 141203 866552 491258 275154 733006 934126 077475 770253 728451 108727 408180 294476 312579 913498 261142 453721 512828 333653 637991 401322 792469 558215 307390 810367 357077 642283 806649 829686 560559 372203 970129 890713 619657 979286 806967 391796 107517 898511 241315 082164 600765 776268 822439 684534 383622 435923 379651 457685 500724 189528 509354 894321 271874 334123 751533 491724 308508 076694 237070 873507 996487 600386 112458 030710 946367 / 473 > 3¹⁰⁴³ [i]