MinT - Best Known (19, 19+57, s)-Nets in Base 128

Best Known (19, 19+57, s)-Nets in Base 128

(19, 19+57, 288)-Net over F₁₂₈ — Constructive and digital

Digital (19, 76, 288)-net over F₁₂₈, using

t-expansion [i] based on digital (9, 76, 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]

(19, 19+57, 386)-Net over F₁₂₈ — Digital

Digital (19, 76, 386)-net over F₁₂₈, using

t-expansion [i] based on digital (15, 76, 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]

(19, 19+57, 39206)-Net in Base 128 — Upper bound on s

There is no (19, 76, 39207)-net in base 128, because

1 times m-reduction [i] would yield (19, 75, 39207)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 109 849722 996355 747224 639519 278865 324659 879411 077576 761946 412257 550876 892131 814537 437697 879213 139642 205172 116643 302286 902266 046953 879926 045005 954137 607793 768284 > 128⁷⁵ [i]