MinT - Best Known (184, 184+51, s)-Nets in Base 3

Best Known (184, 184+51, s)-Nets in Base 3

(184, 184+51, 688)-Net over F₃ — Constructive and digital

Digital (184, 235, 688)-net over F₃, using

1 times m-reduction [i] based on digital (184, 236, 688)-net over F₃, using
- trace code for nets [i] based on digital (7, 59, 172)-net over F₈₁, using
  - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
      - a function field by SÃ©mirat [i]

(184, 184+51, 1727)-Net over F₃ — Digital

Digital (184, 235, 1727)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(184, 184+51, 148723)-Net in Base 3 — Upper bound on s

There is no (184, 235, 148724)-net in base 3, because

1 times m-reduction [i] would yield (184, 234, 148724)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4430 155425 431879 483168 995749 975264 513727 677862 486163 142698 270901 248208 951745 789507 522823 173915 143860 308044 238569 > 3²³⁴ [i]