MinT - Best Known (25, 78, s)-Nets in Base 128

Best Known (25, 78, s)-Nets in Base 128

(25, 78, 288)-Net over F₁₂₈ — Constructive and digital

Digital (25, 78, 288)-net over F₁₂₈, using

t-expansion [i] based on digital (9, 78, 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]

(25, 78, 513)-Net over F₁₂₈ — Digital

Digital (25, 78, 513)-net over F₁₂₈, using

t-expansion [i] based on digital (24, 78, 513)-net over F₁₂₈, using
- net from sequence [i] based on digital (24, 512)-sequence over F₁₂₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 24 and N(F) ≥ 513, using
    - a curve from the manYPoints database [i]

(25, 78, 144555)-Net in Base 128 — Upper bound on s

There is no (25, 78, 144556)-net in base 128, because

1 times m-reduction [i] would yield (25, 77, 144556)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 1 799737 806774 836158 169611 439077 757561 628174 572418 765477 355417 344842 581115 995187 199470 048869 059890 526858 330346 345848 328344 146377 046253 409701 233469 043009 602982 446286 > 128⁷⁷ [i]