MinT - Best Known (24, 24+45, s)-Nets in Base 128

Best Known (24, 24+45, s)-Nets in Base 128

(24, 24+45, 300)-Net over F₁₂₈ — Constructive and digital

Digital (24, 69, 300)-net over F₁₂₈, using

(u,Â u+v)-construction [i] based on
1. digital (1, 23, 150)-net over F₁₂₈, using
  - net from sequence [i] based on digital (1, 149)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 1 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]
2. digital (1, 46, 150)-net over F₁₂₈, using
  - net from sequence [i] based on digital (1, 149)-sequence over F₁₂₈ (see above)

(24, 24+45, 513)-Net over F₁₂₈ — Digital

Digital (24, 69, 513)-net over F₁₂₈, using

net from sequence [i] based on digital (24, 512)-sequence over F₁₂₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 24 and N(F) ≥ 513, using
  - a curve from the manYPoints database [i]

(24, 24+45, 232393)-Net in Base 128 — Upper bound on s

There is no (24, 69, 232394)-net in base 128, because

1 times m-reduction [i] would yield (24, 68, 232394)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 195120 145586 328966 424242 426881 071655 198834 006916 340336 657903 969471 091767 296687 477436 535506 487113 145617 223079 854029 840757 983714 127169 552800 597136 > 128⁶⁸ [i]