MinT - Best Known (14, 14+60, s)-Nets in Base 128

Best Known (14, 14+60, s)-Nets in Base 128

(14, 14+60, 288)-Net over F₁₂₈ — Constructive and digital

Digital (14, 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]

(14, 14+60, 353)-Net over F₁₂₈ — Digital

Digital (14, 74, 353)-net over F₁₂₈, using

net from sequence [i] based on digital (14, 352)-sequence over F₁₂₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 14 and N(F) ≥ 353, using
  - a curve from the manYPoints database [i]

(14, 14+60, 14939)-Net in Base 128 — Upper bound on s

There is no (14, 74, 14940)-net in base 128, because

the generalized Rao bound for nets shows that 128^mÂ â‰¥ 858641 518002 916840 732117 590795 031247 978111 371011 484371 142783 028101 210553 264988 080414 270069 607043 105068 881673 854790 851773 614889 142004 747443 062190 327433 888144 > 128⁷⁴ [i]