MinT - Best Known (48−36, 48, s)-Nets in Base 128

Best Known (48−36, 48, s)-Nets in Base 128

(48−36, 48, 288)-Net over F₁₂₈ — Constructive and digital

Digital (12, 48, 288)-net over F₁₂₈, using

t-expansion [i] based on digital (9, 48, 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]

(48−36, 48, 321)-Net over F₁₂₈ — Digital

Digital (12, 48, 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]

(48−36, 48, 24740)-Net in Base 128 — Upper bound on s

There is no (12, 48, 24741)-net in base 128, because

the generalized Rao bound for nets shows that 128^mÂ â‰¥ 140076 818314 700766 609428 545281 473968 814912 609537 043529 849590 029763 892338 577891 200483 235168 280577 503380 > 128⁴⁸ [i]