MinT - Best Known (151, ∞, s)-Nets in Base 3

Best Known (151, ∞, s)-Nets in Base 3

Digital (151, m, 81)-net over F₃ for arbitrarily large m, using

net from sequence [i] based on digital (151, 80)-sequence over F₃, using
- t-expansion [i] based on digital (144, 80)-sequence over F₃, using
  - base reduction for sequences [i] based on digital (32, 80)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
      - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

Digital (151, m, 163)-net over F₃ for arbitrarily large m, using

There is no (151, m, 317)-net in base 3 for arbitrarily large m, because

m-reduction [i] would yield (151, 1578, 317)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3¹⁵⁷⁸, 317, S₃, 5, 1427), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 243948 654472 259374 792271 833263 306466 822531 674719 681819 081958 973026 262423 435140 242555 404432 059088 571031 214621 744955 816618 522967 818915 563745 676245 192367 740529 502739 878008 409044 842147 123595 224863 679904 831373 938218 467393 956947 135265 682473 993002 769831 991015 103098 002528 704607 594678 469348 202754 562680 540321 168049 591684 501982 038305 870770 524782 053068 820292 606406 905988 381250 031970 691325 143266 556309 714876 629384 594612 240941 157283 691438 933206 741187 776801 800271 068238 371351 218921 015003 104397 574342 460675 005214 824644 326557 563037 020461 629122 881389 983829 353598 836245 209661 056415 870748 771593 321753 111261 290177 473727 251460 553949 191421 892045 848388 292353 636935 262429 417680 409467 507407 549451 992477 662625 852524 562196 758031 884735 342474 822592 223382 414160 520250 613636 063161 714301 / 238 > 3¹⁵⁷⁸ [i]