MinT - Best Known (8, 8+57, s)-Nets in Base 128

Best Known (8, 8+57, s)-Nets in Base 128

(8, 8+57, 216)-Net over F₁₂₈ — Constructive and digital

Digital (8, 65, 216)-net over F₁₂₈, using

t-expansion [i] based on digital (5, 65, 216)-net over F₁₂₈, using
- net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
    - a function field by SÃ©mirat [i]

(8, 8+57, 276)-Net over F₁₂₈ — Digital

Digital (8, 65, 276)-net over F₁₂₈, using

net from sequence [i] based on digital (8, 275)-sequence over F₁₂₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 8 and N(F) ≥ 276, using
  - a curve from the manYPoints database [i]

(8, 8+57, 5816)-Net in Base 128 — Upper bound on s

There is no (8, 65, 5817)-net in base 128, because

1 times m-reduction [i] would yield (8, 64, 5817)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 728 740371 012938 302905 417822 930284 580561 176686 113472 591988 389515 016231 621022 824776 122832 396613 576925 675344 955725 153403 827842 959926 859032 > 128⁶⁴ [i]