MinT - Best Known (8, 67, s)-Nets in Base 128

Best Known (8, 67, s)-Nets in Base 128

(8, 67, 216)-Net over F₁₂₈ — Constructive and digital

Digital (8, 67, 216)-net over F₁₂₈, using

t-expansion [i] based on digital (5, 67, 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]

(8, 67, 276)-Net over F₁₂₈ — Digital

Digital (8, 67, 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]

(8, 67, 5727)-Net in Base 128 — Upper bound on s

There is no (8, 67, 5728)-net in base 128, because

1 times m-reduction [i] would yield (8, 66, 5728)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 11 942294 954920 443290 840773 021529 430429 876204 866248 973764 839033 189093 587030 137282 113727 745144 010984 224958 921225 574979 874130 983536 416956 275659 > 128⁶⁶ [i]