MinT - Best Known (154, ∞, s)-Nets in Base 3

Best Known (154, ∞, s)-Nets in Base 3

Digital (154, m, 81)-net over F₃ for arbitrarily large m, using

net from sequence [i] based on digital (154, 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 (154, m, 163)-net over F₃ for arbitrarily large m, using

net from sequence [i] based on digital (154, 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 (154, m, 323)-net in base 3 for arbitrarily large m, because

m-reduction [i] would yield (154, 1608, 323)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3¹⁶⁰⁸, 323, S₃, 5, 1454), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 98 990810 896881 046782 134097 125274 420684 472691 539921 409678 668158 643973 428139 822080 024684 215054 117768 021082 442456 383522 570324 437933 695372 748164 274063 005092 681457 714515 963149 595208 416379 372663 256660 091680 483267 759214 121027 583316 882250 812329 461365 152271 681672 548685 372054 333296 141480 153151 169114 530099 954302 106815 194425 330344 813096 235009 052530 333609 580966 152130 105808 232400 922437 754296 710668 621711 620305 129864 342257 400176 657495 042374 479773 061792 324776 057329 475615 534702 281048 899775 281798 029272 393606 002051 993081 606419 143463 330580 411122 810793 516550 112019 834739 975316 844365 303043 420115 717026 992225 022403 963504 740243 709355 584550 313823 723096 170441 702421 726733 095929 342649 107166 890499 432912 557772 214257 472723 636757 736353 795229 764560 340343 566076 825668 017416 415397 436270 304672 443649 / 485 > 3¹⁶⁰⁸ [i]