MinT - Best Known (12, 12+62, s)-Nets in Base 128

Best Known (12, 12+62, s)-Nets in Base 128

(12, 12+62, 288)-Net over F₁₂₈ — Constructive and digital

Digital (12, 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]

(12, 12+62, 321)-Net over F₁₂₈ — Digital

Digital (12, 74, 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+62, 10464)-Net in Base 128 — Upper bound on s

There is no (12, 74, 10465)-net in base 128, because

the generalized Rao bound for nets shows that 128^mÂ â‰¥ 859808 155681 334451 011308 899414 817250 211893 120570 587805 682913 048391 355444 368384 752658 231192 929269 499206 954919 377491 801757 009481 719458 268417 888964 979266 050208 > 128⁷⁴ [i]