MinT - Best Known (247−57, 247, s)-Nets in Base 3

Best Known (247−57, 247, s)-Nets in Base 3

(247−57, 247, 600)-Net over F₃ — Constructive and digital

Digital (190, 247, 600)-net over F₃, using

1 times m-reduction [i] based on digital (190, 248, 600)-net over F₃, using
- trace code for nets [i] based on digital (4, 62, 150)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(247−57, 247, 1403)-Net over F₃ — Digital

Digital (190, 247, 1403)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(247−57, 247, 87839)-Net in Base 3 — Upper bound on s

There is no (190, 247, 87840)-net in base 3, because

1 times m-reduction [i] would yield (190, 246, 87840)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2354 453513 747511 935594 842026 404004 095899 253662 266501 599716 756142 023434 878994 688931 934517 437440 826552 922416 760862 526209 > 3²⁴⁶ [i]