MinT - Best Known (24, 24+47, s)-Nets in Base 128

Best Known (24, 24+47, s)-Nets in Base 128

(24, 24+47, 288)-Net over F₁₂₈ — Constructive and digital

Digital (24, 71, 288)-net over F₁₂₈, using

t-expansion [i] based on digital (9, 71, 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, 24+47, 513)-Net over F₁₂₈ — Digital

Digital (24, 71, 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, 24+47, 192253)-Net in Base 128 — Upper bound on s

There is no (24, 71, 192254)-net in base 128, because

1 times m-reduction [i] would yield (24, 70, 192254)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 3196 729571 146085 810289 644821 990123 704930 871209 508273 287671 334848 344822 598005 940964 671850 502671 183359 874462 486018 247333 815188 357845 628102 697303 069420 > 128⁷⁰ [i]