MinT - Best Known (74−66, 74, s)-Nets in Base 128

Best Known (74−66, 74, s)-Nets in Base 128

(74−66, 74, 216)-Net over F₁₂₈ — Constructive and digital

Digital (8, 74, 216)-net over F₁₂₈, using

t-expansion [i] based on digital (5, 74, 216)-net over F₁₂₈, using
- net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
    - a function field by SÃ©mirat [i]

(74−66, 74, 276)-Net over F₁₂₈ — Digital

Digital (8, 74, 276)-net over F₁₂₈, using

net from sequence [i] based on digital (8, 275)-sequence over F₁₂₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 8 and N(F) ≥ 276, using
  - a curve from the manYPoints database [i]

(74−66, 74, 5489)-Net in Base 128 — Upper bound on s

There is no (8, 74, 5490)-net in base 128, because

the generalized Rao bound for nets shows that 128^mÂ â‰¥ 861162 017778 777031 047905 179380 774873 792011 188573 774689 858345 072812 357624 582678 427162 202938 741127 003438 296238 122075 622202 935335 485965 497462 494291 946937 770367 > 128⁷⁴ [i]