MinT - Best Known (71−55, 71, s)-Nets in Base 128

Best Known (71−55, 71, s)-Nets in Base 128

(71−55, 71, 288)-Net over F₁₂₈ — Constructive and digital

Digital (16, 71, 288)-net over F₁₂₈, using

t-expansion [i] based on digital (9, 71, 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]

(71−55, 71, 386)-Net over F₁₂₈ — Digital

Digital (16, 71, 386)-net over F₁₂₈, using

t-expansion [i] based on digital (15, 71, 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]

(71−55, 71, 24975)-Net in Base 128 — Upper bound on s

There is no (16, 71, 24976)-net in base 128, because

1 times m-reduction [i] would yield (16, 70, 24976)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 3199 163922 043527 502958 274855 359185 151856 856473 588067 990857 073523 299327 830125 288783 531182 350346 870176 768460 660922 491983 376624 416268 660234 877895 824424 > 128⁷⁰ [i]