MinT - Best Known (183, 183+55, s)-Nets in Base 3

Best Known (183, 183+55, s)-Nets in Base 3

(183, 183+55, 600)-Net over F₃ — Constructive and digital

Digital (183, 238, 600)-net over F₃, using

3² times duplication [i] based on digital (181, 236, 600)-net over F₃, using
- trace code for nets [i] based on digital (4, 59, 150)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(183, 183+55, 1353)-Net over F₃ — Digital

Digital (183, 238, 1353)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(183, 183+55, 84198)-Net in Base 3 — Upper bound on s

There is no (183, 238, 84199)-net in base 3, because

1 times m-reduction [i] would yield (183, 237, 84199)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 119619 986225 789128 334589 942179 767861 000825 672825 946178 074646 584547 809336 939496 169688 888666 164804 825302 906068 944619 > 3²³⁷ [i]