MinT - Best Known (6, 56, s)-Nets in Base 128

Best Known (6, 56, s)-Nets in Base 128

(6, 56, 216)-Net over F₁₂₈ — Constructive and digital

Digital (6, 56, 216)-net over F₁₂₈, using

t-expansion [i] based on digital (5, 56, 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]

(6, 56, 243)-Net over F₁₂₈ — Digital

Digital (6, 56, 243)-net over F₁₂₈, using

net from sequence [i] based on digital (6, 242)-sequence over F₁₂₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 6 and N(F) ≥ 243, using
  - a curve from the manYPoints database [i]

(6, 56, 4194)-Net in Base 128 — Upper bound on s

There is no (6, 56, 4195)-net in base 128, because

the generalized Rao bound for nets shows that 128^mÂ â‰¥ 10098 357843 142984 498468 242545 143088 180732 586363 887612 601698 195339 294455 442999 431143 780146 276886 772288 766630 521803 982072 > 128⁵⁶ [i]