MinT - Best Known (156, 156+∞, s)-Nets in Base 3

Best Known (156, 156+∞, s)-Nets in Base 3

Digital (156, m, 81)-net over F₃ for arbitrarily large m, using

net from sequence [i] based on digital (156, 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 (156, m, 163)-net over F₃ for arbitrarily large m, using

net from sequence [i] based on digital (156, 162)-sequence over F₃, using
- t-expansion [i] based on digital (151, 162)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 151 and N(F) ≥ 163, using
    - Drinfeld modules of rank 1 [i]

There is no (156, m, 327)-net in base 3 for arbitrarily large m, because

m-reduction [i] would yield (156, 1628, 327)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3¹⁶²⁸, 327, S₃, 5, 1472), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 341759 027934 949341 615624 529481 141794 927453 969843 095618 949436 562369 729912 518136 163471 103279 883384 571797 646437 427938 601299 011693 669737 149235 567084 383563 471514 278178 344776 781652 117420 126489 702375 560599 375263 673729 217429 875855 288702 498962 197974 465565 351151 543576 106205 593704 743594 316866 496433 892387 997675 329611 703526 099097 660683 829053 009952 146639 993358 622276 241405 993987 540969 191765 948884 425995 336521 023018 206526 274260 298618 638446 949360 515830 430418 291956 578591 901699 561136 629678 584175 668612 254207 903809 650579 098763 259312 660296 348965 712393 584195 545379 561763 729865 561603 404247 107805 182854 781645 141957 814793 641621 752886 042391 253332 211244 746057 016315 379685 221601 768229 448104 768986 751313 564282 462417 560696 176267 910364 198183 491047 030834 305283 904704 876230 275679 110110 923845 715419 605452 357483 / 491 > 3¹⁶²⁸ [i]