MinT - Best Known (183, 183+54, s)-Nets in Base 3

Best Known (183, 183+54, s)-Nets in Base 3

(183, 183+54, 640)-Net over F₃ — Constructive and digital

Digital (183, 237, 640)-net over F₃, using

3¹ times duplication [i] based on digital (182, 236, 640)-net over F₃, using
- trace code for nets [i] based on digital (5, 59, 160)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
      - a function field by SÃ©mirat [i]

(183, 183+54, 1427)-Net over F₃ — Digital

Digital (183, 237, 1427)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(183, 183+54, 84198)-Net in Base 3 — Upper bound on s

There is no (183, 237, 84199)-net in base 3, because

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]