MinT - Best Known (231−146, 231, s)-Nets in Base 3

Best Known (231−146, 231, s)-Nets in Base 3

(231−146, 231, 60)-Net over F₃ — Constructive and digital

Digital (85, 231, 60)-net over F₃, using

net from sequence [i] based on digital (85, 59)-sequence over F₃, using
- base reduction for sequences [i] based on digital (13, 59)-sequence over F₉, using
  - s-reduction based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(231−146, 231, 84)-Net over F₃ — Digital

Digital (85, 231, 84)-net over F₃, using

t-expansion [i] based on digital (71, 231, 84)-net over F₃, using
- net from sequence [i] based on digital (71, 83)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 71 and N(F) ≥ 84, using
    - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]

(231−146, 231, 384)-Net in Base 3 — Upper bound on s

There is no (85, 231, 385)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 167 388465 647247 039735 721874 154753 702320 172230 921427 532388 266684 459967 902510 106459 511350 210254 742537 566687 592163 > 3²³¹ [i]