MinT - Best Known (4, 4+26, s)-Nets in Base 128

Best Known (4, 4+26, s)-Nets in Base 128

(4, 4+26, 192)-Net over F₁₂₈ — Constructive and digital

Digital (4, 30, 192)-net over F₁₂₈, using

t-expansion [i] based on digital (3, 30, 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]

(4, 4+26, 215)-Net over F₁₂₈ — Digital

Digital (4, 30, 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]

(4, 4+26, 257)-Net in Base 128 — Constructive

(4, 30, 257)-net in base 128, using

2 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]

(4, 4+26, 3247)-Net in Base 128 — Upper bound on s

There is no (4, 30, 3248)-net in base 128, because

the generalized Rao bound for nets shows that 128^mÂ â‰¥ 1647 288725 393321 269298 475381 956145 304718 081570 806600 857956 583411 > 128³⁰ [i]