MinT - Best Known (178, 178+55, s)-Nets in Base 3

Best Known (178, 178+55, s)-Nets in Base 3

(178, 178+55, 464)-Net over F₃ — Constructive and digital

Digital (178, 233, 464)-net over F₃, using

3¹ times duplication [i] based on digital (177, 232, 464)-net over F₃, using
- t-expansion [i] based on digital (176, 232, 464)-net over F₃, using
  - trace code for nets [i] based on digital (2, 58, 116)-net over F₈₁, using
    - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
        a function field by SÃ©mirat [i]

(178, 178+55, 1216)-Net over F₃ — Digital

Digital (178, 233, 1216)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(178, 178+55, 68693)-Net in Base 3 — Upper bound on s

There is no (178, 233, 68694)-net in base 3, because

1 times m-reduction [i] would yield (178, 232, 68694)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 492 217161 872604 153924 711330 566874 513239 661783 667563 288836 245254 043995 429360 089717 409963 305311 734678 387289 737009 > 3²³² [i]