MinT - Best Known (78−58, 78, s)-Nets in Base 128

Best Known (78−58, 78, s)-Nets in Base 128

(78−58, 78, 288)-Net over F₁₂₈ — Constructive and digital

Digital (20, 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]

(78−58, 78, 386)-Net over F₁₂₈ — Digital

Digital (20, 78, 386)-net over F₁₂₈, using

t-expansion [i] based on digital (15, 78, 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]

(78−58, 78, 42740)-Net in Base 128 — Upper bound on s

There is no (20, 78, 42741)-net in base 128, because

the generalized Rao bound for nets shows that 128^mÂ â‰¥ 230 386221 154350 489096 964518 266039 760641 104332 893572 942435 317389 159243 360254 798731 531793 530303 508273 241722 475705 528273 636160 415111 753569 914828 569125 426957 521999 919456 > 128⁷⁸ [i]