MinT - Best Known (12, 57, s)-Nets in Base 128

Best Known (12, 57, s)-Nets in Base 128

(12, 57, 288)-Net over F₁₂₈ — Constructive and digital

Digital (12, 57, 288)-net over F₁₂₈, using

t-expansion [i] based on digital (9, 57, 288)-net over F₁₂₈, using
- net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
    - a function field by SÃ©mirat [i]

(12, 57, 321)-Net over F₁₂₈ — Digital

Digital (12, 57, 321)-net over F₁₂₈, using

net from sequence [i] based on digital (12, 320)-sequence over F₁₂₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 12 and N(F) ≥ 321, using
  - a curve from the manYPoints database [i]

(12, 57, 16465)-Net in Base 128 — Upper bound on s

There is no (12, 57, 16466)-net in base 128, because

1 times m-reduction [i] would yield (12, 56, 16466)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 10093 554378 732105 186618 194734 803665 900355 573843 301427 828187 157236 776832 994188 624310 473697 458258 774473 583059 308780 431072 > 128⁵⁶ [i]