MinT - Best Known (12, 12+48, s)-Nets in Base 128

Best Known (12, 12+48, s)-Nets in Base 128

(12, 12+48, 288)-Net over F₁₂₈ — Constructive and digital

Digital (12, 60, 288)-net over F₁₂₈, using

t-expansion [i] based on digital (9, 60, 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]

(12, 12+48, 321)-Net over F₁₂₈ — Digital

Digital (12, 60, 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]

(12, 12+48, 14296)-Net in Base 128 — Upper bound on s

There is no (12, 60, 14297)-net in base 128, because

the generalized Rao bound for nets shows that 128^mÂ â‰¥ 2 710057 773470 227732 318168 804412 014562 704925 463640 439216 304938 586812 555637 072242 329981 740742 536201 143153 581413 232154 400445 194637 > 128⁶⁰ [i]