MinT - Best Known (15, 15+62, s)-Nets in Base 128

Best Known (15, 15+62, s)-Nets in Base 128

(15, 15+62, 288)-Net over F₁₂₈ — Constructive and digital

Digital (15, 77, 288)-net over F₁₂₈, using

t-expansion [i] based on digital (9, 77, 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]

(15, 15+62, 386)-Net over F₁₂₈ — Digital

Digital (15, 77, 386)-net over F₁₂₈, using

net from sequence [i] based on digital (15, 385)-sequence over F₁₂₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 15 and N(F) ≥ 386, using
  - a curve from the manYPoints database [i]

(15, 15+62, 16744)-Net in Base 128 — Upper bound on s

There is no (15, 77, 16745)-net in base 128, because

the generalized Rao bound for nets shows that 128^mÂ â‰¥ 1 801283 236040 428114 165165 728427 027638 838600 818947 669652 141753 011213 457498 977209 091904 096708 906710 077917 915449 455738 917689 634452 017812 595601 998583 179468 573872 875424 > 128⁷⁷ [i]