MinT - Best Known (6, 61, s)-Nets in Base 128

Best Known (6, 61, s)-Nets in Base 128

(6, 61, 216)-Net over F₁₂₈ — Constructive and digital

Digital (6, 61, 216)-net over F₁₂₈, using

t-expansion [i] based on digital (5, 61, 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, 61, 243)-Net over F₁₂₈ — Digital

Digital (6, 61, 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, 61, 4129)-Net in Base 128 — Upper bound on s

There is no (6, 61, 4130)-net in base 128, because

1 times m-reduction [i] would yield (6, 60, 4130)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 2 715188 325039 337156 221100 665065 398616 769504 865613 317942 555407 470396 470240 916627 013372 415300 213505 040508 550679 697734 809334 079888 > 128⁶⁰ [i]