MinT - Best Known (178, 178+57, s)-Nets in Base 3

Best Known (178, 178+57, s)-Nets in Base 3

(178, 178+57, 400)-Net over F₃ — Constructive and digital

Digital (178, 235, 400)-net over F₃, using

1 times m-reduction [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]

(178, 178+57, 1095)-Net over F₃ — Digital

Digital (178, 235, 1095)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(178, 178+57, 54843)-Net in Base 3 — Upper bound on s

There is no (178, 235, 54844)-net in base 3, because

1 times m-reduction [i] would yield (178, 234, 54844)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4430 054709 583733 043879 894388 468400 522959 490436 994317 388654 556480 482837 228922 976533 995706 497988 782200 645915 433665 > 3²³⁴ [i]