MinT - Best Known (178−44, 178, s)-Nets in Base 3

Best Known (178−44, 178, s)-Nets in Base 3

(178−44, 178, 328)-Net over F₃ — Constructive and digital

Digital (134, 178, 328)-net over F₃, using

3² times duplication [i] based on digital (132, 176, 328)-net over F₃, using
- trace code for nets [i] based on digital (0, 44, 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]

(178−44, 178, 810)-Net over F₃ — Digital

Digital (134, 178, 810)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(178−44, 178, 32800)-Net in Base 3 — Upper bound on s

There is no (134, 178, 32801)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8 465800 925787 715740 538895 915402 602806 889393 286153 299753 140825 108071 310933 798324 911449 > 3¹⁷⁸ [i]