MinT - Best Known (74−61, 74, s)-Nets in Base 128

Best Known (74−61, 74, s)-Nets in Base 128

(74−61, 74, 288)-Net over F₁₂₈ — Constructive and digital

Digital (13, 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]

(74−61, 74, 321)-Net over F₁₂₈ — Digital

Digital (13, 74, 321)-net over F₁₂₈, using

t-expansion [i] based on digital (12, 74, 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]

(74−61, 74, 12706)-Net in Base 128 — Upper bound on s

There is no (13, 74, 12707)-net in base 128, because

1 times m-reduction [i] would yield (13, 73, 12707)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 6711 813085 134732 341104 546898 661137 369023 423605 464914 744432 657721 459728 537915 357173 725103 917372 442949 127278 829268 536065 387947 685718 212886 366052 788036 211400 > 128⁷³ [i]