MinT - Best Known (238−47, 238, s)-Nets in Base 3

Best Known (238−47, 238, s)-Nets in Base 3

(238−47, 238, 688)-Net over F₃ — Constructive and digital

Digital (191, 238, 688)-net over F₃, using

t-expansion [i] based on digital (190, 238, 688)-net over F₃, using
- 6 times m-reduction [i] based on digital (190, 244, 688)-net over F₃, using
  - trace code for nets [i] based on digital (7, 61, 172)-net over F₈₁, using
    - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
        a function field by SÃ©mirat [i]

(238−47, 238, 2670)-Net over F₃ — Digital

Digital (191, 238, 2670)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(238−47, 238, 388887)-Net in Base 3 — Upper bound on s

There is no (191, 238, 388888)-net in base 3, because

1 times m-reduction [i] would yield (191, 237, 388888)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 119601 833032 729459 445536 992959 614631 220361 823430 835681 416260 322140 076779 335932 693642 979154 898017 399404 009234 784289 > 3²³⁷ [i]