MinT - Best Known (26, 71, s)-Nets in Base 128

Best Known (26, 71, s)-Nets in Base 128

(26, 71, 342)-Net over F₁₂₈ — Constructive and digital

Digital (26, 71, 342)-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 (3, 48, 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]

(26, 71, 513)-Net over F₁₂₈ — Digital

Digital (26, 71, 513)-net over F₁₂₈, using

t-expansion [i] based on digital (24, 71, 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]

(26, 71, 361239)-Net in Base 128 — Upper bound on s

There is no (26, 71, 361240)-net in base 128, because

1 times m-reduction [i] would yield (26, 70, 361240)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 3196 729579 374888 765167 275459 041794 912809 004992 256313 379880 871883 000123 552093 931394 745984 956224 839236 285009 563327 229615 132924 369683 084218 105221 827399 > 128⁷⁰ [i]