MinT - Best Known (24, 77, s)-Nets in Base 128

Best Known (24, 77, s)-Nets in Base 128

(24, 77, 288)-Net over F₁₂₈ — Constructive and digital

Digital (24, 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]

(24, 77, 513)-Net over F₁₂₈ — Digital

Digital (24, 77, 513)-net over F₁₂₈, using

net from sequence [i] based on digital (24, 512)-sequence over F₁₂₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 24 and N(F) ≥ 513, using
  - a curve from the manYPoints database [i]

(24, 77, 119944)-Net in Base 128 — Upper bound on s

There is no (24, 77, 119945)-net in base 128, because

1 times m-reduction [i] would yield (24, 76, 119945)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 14060 783629 918042 068612 563536 602885 356811 220208 397642 898936 052326 695830 998812 192760 354886 838752 356826 190405 711784 130323 124425 482950 856789 585333 929052 589628 437312 > 128⁷⁶ [i]