MinT - Best Known (179, 179+59, s)-Nets in Base 3

Best Known (179, 179+59, s)-Nets in Base 3

(179, 179+59, 328)-Net over F₃ — Constructive and digital

Digital (179, 238, 328)-net over F₃, using

3² times duplication [i] based on digital (177, 236, 328)-net over F₃, using
- trace code for nets [i] based on digital (0, 59, 82)-net over F₈₁, using
  - net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
      - the rational function field F₈₁(x) [i]
    - Niederreiter sequence [i]

(179, 179+59, 1014)-Net over F₃ — Digital

Digital (179, 238, 1014)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(179, 179+59, 46244)-Net in Base 3 — Upper bound on s

There is no (179, 238, 46245)-net in base 3, because

1 times m-reduction [i] would yield (179, 237, 46245)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 119665 013917 264449 530124 850791 217865 790039 601849 979702 332586 992778 496944 965696 517603 571075 587563 916775 727379 648251 > 3²³⁷ [i]