MinT - Best Known (179, 179+58, s)-Nets in Base 3

Best Known (179, 179+58, s)-Nets in Base 3

(179, 179+58, 400)-Net over F₃ — Constructive and digital

Digital (179, 237, 400)-net over F₃, using

3¹ times duplication [i] based on digital (178, 236, 400)-net over F₃, using
- trace code for nets [i] based on digital (1, 59, 100)-net over F₈₁, using
  - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]

(179, 179+58, 1064)-Net over F₃ — Digital

Digital (179, 237, 1064)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(179, 179+58, 46244)-Net in Base 3 — Upper bound on s

There is no (179, 237, 46245)-net in base 3, because

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]