MinT - Best Known (176, 233, s)-Nets in Base 3

Best Known (176, 233, s)-Nets in Base 3

(176, 233, 400)-Net over F₃ — Constructive and digital

Digital (176, 233, 400)-net over F₃, using

3¹ times duplication [i] based on digital (175, 232, 400)-net over F₃, using
- trace code for nets [i] based on digital (1, 58, 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]

(176, 233, 1050)-Net over F₃ — Digital

Digital (176, 233, 1050)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(176, 233, 50702)-Net in Base 3 — Upper bound on s

There is no (176, 233, 50703)-net in base 3, because

1 times m-reduction [i] would yield (176, 232, 50703)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 492 304221 602617 385359 310734 894470 588166 946822 126568 389151 501035 774760 904652 855313 309154 008393 276951 509330 311369 > 3²³² [i]