MinT - Best Known (77, 177, s)-Nets in Base 3

Best Known (77, 177, s)-Nets in Base 3

(77, 177, 52)-Net over F₃ — Constructive and digital

Digital (77, 177, 52)-net over F₃, using

net from sequence [i] based on digital (77, 51)-sequence over F₃, using
- base reduction for sequences [i] based on digital (13, 51)-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]

(77, 177, 84)-Net over F₃ — Digital

Digital (77, 177, 84)-net over F₃, using

t-expansion [i] based on digital (71, 177, 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]

(77, 177, 428)-Net in Base 3 — Upper bound on s

There is no (77, 177, 429)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 952843 313886 608987 898474 803333 862299 649507 634030 142319 544651 417475 298793 081332 398497 > 3¹⁷⁷ [i]