MinT - Best Known (77−57, 77, s)-Nets in Base 128

Best Known (77−57, 77, s)-Nets in Base 128

(77−57, 77, 288)-Net over F₁₂₈ — Constructive and digital

Digital (20, 77, 288)-net over F₁₂₈, using

t-expansion [i] based on digital (9, 77, 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]

(77−57, 77, 386)-Net over F₁₂₈ — Digital

Digital (20, 77, 386)-net over F₁₂₈, using

t-expansion [i] based on digital (15, 77, 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]

(77−57, 77, 46627)-Net in Base 128 — Upper bound on s

There is no (20, 77, 46628)-net in base 128, because

1 times m-reduction [i] would yield (20, 76, 46628)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 14062 123164 298632 548809 594005 844810 327701 595480 319084 234606 391756 094653 274124 899733 314584 284731 703744 375208 370029 216007 093961 097009 093959 270187 640165 400291 629608 > 128⁷⁶ [i]