MinT - Best Known (28−24, 28, s)-Nets in Base 128

Best Known (28−24, 28, s)-Nets in Base 128

(28−24, 28, 192)-Net over F₁₂₈ — Constructive and digital

Digital (4, 28, 192)-net over F₁₂₈, using

t-expansion [i] based on digital (3, 28, 192)-net over F₁₂₈, using
- net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
    - a function field by SÃ©mirat [i]

(28−24, 28, 215)-Net over F₁₂₈ — Digital

Digital (4, 28, 215)-net over F₁₂₈, using

net from sequence [i] based on digital (4, 214)-sequence over F₁₂₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 4 and N(F) ≥ 215, using
  - a curve from the manYPoints database [i]

(28−24, 28, 257)-Net in Base 128 — Constructive

(4, 28, 257)-net in base 128, using

4 times m-reduction [i] based on (4, 32, 257)-net in base 128, using
- base change [i] based on digital (0, 28, 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]

(28−24, 28, 3433)-Net in Base 128 — Upper bound on s

There is no (4, 28, 3434)-net in base 128, because

the generalized Rao bound for nets shows that 128^mÂ â‰¥ 100784 040207 715539 925021 716779 595015 421960 080326 376487 366872 > 128²⁸ [i]