MinT - Best Known (8, 63, s)-Nets in Base 128

Best Known (8, 63, s)-Nets in Base 128

(8, 63, 216)-Net over F₁₂₈ — Constructive and digital

Digital (8, 63, 216)-net over F₁₂₈, using

t-expansion [i] based on digital (5, 63, 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, 63, 257)-Net in Base 128 — Constructive

(8, 63, 257)-net in base 128, using

1 times m-reduction [i] based on (8, 64, 257)-net in base 128, using
- base change [i] based on digital (0, 56, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
      - the rational function field F₂₅₆(x) [i]
    - Niederreiter sequence [i]

(8, 63, 276)-Net over F₁₂₈ — Digital

Digital (8, 63, 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, 63, 5921)-Net in Base 128 — Upper bound on s

There is no (8, 63, 5922)-net in base 128, because

1 times m-reduction [i] would yield (8, 62, 5922)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 44512 932868 348415 899201 496115 837850 722855 546457 793482 424204 473781 208265 336376 723038 365893 514067 545129 732920 993623 460197 249759 058960 > 128⁶² [i]