MinT - Best Known (18, 18+56, s)-Nets in Base 128

Best Known (18, 18+56, s)-Nets in Base 128

(18, 18+56, 288)-Net over F₁₂₈ — Constructive and digital

Digital (18, 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]

(18, 18+56, 386)-Net over F₁₂₈ — Digital

Digital (18, 74, 386)-net over F₁₂₈, using

t-expansion [i] based on digital (15, 74, 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]

(18, 18+56, 32966)-Net in Base 128 — Upper bound on s

There is no (18, 74, 32967)-net in base 128, because

the generalized Rao bound for nets shows that 128^mÂ â‰¥ 858315 290739 347503 304531 066426 179157 774881 758461 698600 182453 125936 491927 478723 201695 402446 252869 645837 302649 117337 926105 863543 021495 472295 476013 883264 864024 > 128⁷⁴ [i]