MinT - Best Known (118, 118+∞, s)-Nets in Base 3

Best Known (118, 118+∞, s)-Nets in Base 3

Digital (118, m, 75)-net over F₃ for arbitrarily large m, using

net from sequence [i] based on digital (118, 74)-sequence over F₃, using
- base reduction for sequences [i] based on digital (22, 74)-sequence over F₉, using
  - s-reduction based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

Digital (118, m, 120)-net over F₃ for arbitrarily large m, using

There is no (118, m, 250)-net in base 3 for arbitrarily large m, because

m-reduction [i] would yield (118, 1493, 250)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3¹⁴⁹³, 250, S₃, 6, 1375), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 9 957068 582222 468714 466637 050264 642193 250493 187906 175239 075596 791965 257390 720426 747823 834864 387640 664780 713910 518634 248534 504598 432990 331260 789802 191275 689130 363971 592499 245163 126240 301139 533121 272591 015899 229039 997244 848913 381665 095054 175409 081136 057993 580369 725781 530111 042740 773992 733078 826597 064986 509367 151383 992571 461072 231878 599664 962103 217135 315712 913681 823771 237376 640715 847420 635221 627850 571963 405400 048750 031384 944183 681147 869025 010226 993844 022864 810891 500062 938737 523742 375878 342450 650507 591612 168717 339050 502010 341466 857505 098053 530841 031653 345999 593054 633834 385718 386237 208533 219441 996795 347509 531882 522212 765284 580559 367176 031829 534281 944045 272415 567119 098307 341332 530606 599437 719554 275686 168295 414719 / 344 > 3¹⁴⁹³ [i]