MinT - Best Known (247−128, 247, s)-Nets in Base 3

Best Known (247−128, 247, s)-Nets in Base 3

(247−128, 247, 76)-Net over F₃ — Constructive and digital

Digital (119, 247, 76)-net over F₃, using

net from sequence [i] based on digital (119, 75)-sequence over F₃, using
- base reduction for sequences [i] based on digital (22, 75)-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]

(247−128, 247, 120)-Net over F₃ — Digital

Digital (119, 247, 120)-net over F₃, using

t-expansion [i] based on digital (113, 247, 120)-net over F₃, using
- net from sequence [i] based on digital (113, 119)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 113 and N(F) ≥ 120, using
    - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]

(247−128, 247, 794)-Net in Base 3 — Upper bound on s

There is no (119, 247, 795)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7257 528650 947695 883947 814993 332906 509560 911621 396217 129653 303001 336482 212049 424952 734353 712613 653294 528235 581488 144257 > 3²⁴⁷ [i]