MinT - Best Known (17, 74, s)-Nets in Base 128

Best Known (17, 74, s)-Nets in Base 128

(17, 74, 288)-Net over F₁₂₈ — Constructive and digital

Digital (17, 74, 288)-net over F₁₂₈, using

t-expansion [i] based on digital (9, 74, 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]

(17, 74, 386)-Net over F₁₂₈ — Digital

Digital (17, 74, 386)-net over F₁₂₈, using

t-expansion [i] based on digital (15, 74, 386)-net over F₁₂₈, using
- net from sequence [i] based on digital (15, 385)-sequence over F₁₂₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 15 and N(F) ≥ 386, using
    - a curve from the manYPoints database [i]

(17, 74, 27719)-Net in Base 128 — Upper bound on s

There is no (17, 74, 27720)-net in base 128, because

1 times m-reduction [i] would yield (17, 73, 27720)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 6707 961372 791577 830467 159495 661563 613697 583102 058069 821413 557911 829756 221309 175049 653345 517090 234941 783641 849191 654246 491683 632622 428393 216277 733026 385384 > 128⁷³ [i]