MinT - Best Known (98, 98+121, s)-Nets in Base 3

Best Known (98, 98+121, s)-Nets in Base 3

(98, 98+121, 65)-Net over F₃ — Constructive and digital

Digital (98, 219, 65)-net over F₃, 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]

(98, 98+121, 96)-Net over F₃ — Digital

Digital (98, 219, 96)-net over F₃, using

t-expansion [i] based on digital (89, 219, 96)-net over F₃, using
- net from sequence [i] based on digital (89, 95)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 89 and N(F) ≥ 96, using
    - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]

(98, 98+121, 570)-Net in Base 3 — Upper bound on s

There is no (98, 219, 571)-net in base 3, because

1 times m-reduction [i] would yield (98, 218, 571)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 107 224425 518007 009690 621488 138074 094350 436889 868656 318961 415976 950175 106528 703309 583033 194680 219298 272617 > 3²¹⁸ [i]