MinT - Best Known (29, 29+47, s)-Nets in Base 128

Best Known (29, 29+47, s)-Nets in Base 128

(29, 29+47, 384)-Net over F₁₂₈ — Constructive and digital

Digital (29, 76, 384)-net over F₁₂₈, using

(u,Â u+v)-construction [i] based on
1. digital (3, 26, 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]
2. digital (3, 50, 192)-net over F₁₂₈, using
  - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈ (see above)

(29, 29+47, 577)-Net over F₁₂₈ — Digital

Digital (29, 76, 577)-net over F₁₂₈, using

t-expansion [i] based on digital (28, 76, 577)-net over F₁₂₈, using
- net from sequence [i] based on digital (28, 576)-sequence over F₁₂₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 28 and N(F) ≥ 577, using
    - a curve from the manYPoints database [i]

(29, 29+47, 552052)-Net in Base 128 — Upper bound on s

There is no (29, 76, 552053)-net in base 128, because

1 times m-reduction [i] would yield (29, 75, 552053)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 109 837659 175049 169480 546104 743362 513383 539891 074124 305488 065346 713627 998796 008424 837066 305066 713877 664623 107050 339797 942443 062292 471693 267882 702450 509159 537376 > 128⁷⁵ [i]