MinT - Best Known (16, 72, s)-Nets in Base 128

Best Known (16, 72, s)-Nets in Base 128

(16, 72, 288)-Net over F₁₂₈ — Constructive and digital

Digital (16, 72, 288)-net over F₁₂₈, using

t-expansion [i] based on digital (9, 72, 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]

(16, 72, 386)-Net over F₁₂₈ — Digital

Digital (16, 72, 386)-net over F₁₂₈, using

t-expansion [i] based on digital (15, 72, 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]

(16, 72, 23306)-Net in Base 128 — Upper bound on s

There is no (16, 72, 23307)-net in base 128, because

the generalized Rao bound for nets shows that 128^mÂ â‰¥ 52 376629 052468 811223 824606 581239 485597 980282 675178 929784 989060 254900 701852 444094 376262 037485 926971 463545 976912 623736 284314 044014 771097 262764 460433 627072 > 128⁷² [i]