MinT - Best Known (176, 176+58, s)-Nets in Base 3

Best Known (176, 176+58, s)-Nets in Base 3

(176, 176+58, 328)-Net over F₃ — Constructive and digital

Digital (176, 234, 328)-net over F₃, using

3² times duplication [i] based on digital (174, 232, 328)-net over F₃, using
- trace code for nets [i] based on digital (0, 58, 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]

(176, 176+58, 1001)-Net over F₃ — Digital

Digital (176, 234, 1001)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(176, 176+58, 41273)-Net in Base 3 — Upper bound on s

There is no (176, 234, 41274)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4432 435298 841336 626871 886677 356992 828884 250582 172175 562337 119959 159054 000189 499538 269147 516704 331687 528301 192669 > 3²³⁴ [i]