MinT - Best Known (76−63, 76, s)-Nets in Base 128

Best Known (76−63, 76, s)-Nets in Base 128

(76−63, 76, 288)-Net over F₁₂₈ — Constructive and digital

Digital (13, 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]

(76−63, 76, 321)-Net over F₁₂₈ — Digital

Digital (13, 76, 321)-net over F₁₂₈, using

t-expansion [i] based on digital (12, 76, 321)-net over F₁₂₈, using
- net from sequence [i] based on digital (12, 320)-sequence over F₁₂₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 12 and N(F) ≥ 321, using
    - a curve from the manYPoints database [i]

(76−63, 76, 12239)-Net in Base 128 — Upper bound on s

There is no (13, 76, 12240)-net in base 128, because

1 times m-reduction [i] would yield (13, 75, 12240)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 109 867844 266792 594964 178180 600953 923089 383663 468605 881519 550477 359262 649930 010725 165060 401507 025057 425297 855076 105878 401105 418760 246987 305505 863201 067837 549012 > 128⁷⁵ [i]