MinT - Best Known (28, 28+48, s)-Nets in Base 128

Best Known (28, 28+48, s)-Nets in Base 128

(28, 28+48, 342)-Net over F₁₂₈ — Constructive and digital

Digital (28, 76, 342)-net over F₁₂₈, using

(u,Â u+v)-construction [i] based on
1. digital (1, 25, 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, 51, 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, 28+48, 577)-Net over F₁₂₈ — Digital

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]

(28, 28+48, 363393)-Net in Base 128 — Upper bound on s

There is no (28, 76, 363394)-net in base 128, because

the generalized Rao bound for nets shows that 128^mÂ â‰¥ 14059 988078 291764 835322 141465 759764 008981 691116 196439 479315 169337 560562 533667 405863 776846 928766 885366 797469 669120 489374 429200 047762 490269 137563 767330 463297 756464 > 128⁷⁶ [i]