MinT - Best Known (228−128, 228, s)-Nets in Base 3

Best Known (228−128, 228, s)-Nets in Base 3

(228−128, 228, 67)-Net over F₃ — Constructive and digital

Digital (100, 228, 67)-net over F₃, using

net from sequence [i] based on digital (100, 66)-sequence over F₃, using
- base reduction for sequences [i] based on digital (17, 66)-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]

(228−128, 228, 96)-Net over F₃ — Digital

Digital (100, 228, 96)-net over F₃, using

t-expansion [i] based on digital (89, 228, 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]

(228−128, 228, 557)-Net in Base 3 — Upper bound on s

There is no (100, 228, 558)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6 722689 082073 959405 315535 269825 369035 812563 453453 280980 359463 537444 613860 939672 589813 935055 899623 900117 927553 > 3²²⁸ [i]