MinT - Best Known (46−33, 46, s)-Nets in Base 128

Best Known (46−33, 46, s)-Nets in Base 128

(46−33, 46, 288)-Net over F₁₂₈ — Constructive and digital

Digital (13, 46, 288)-net over F₁₂₈, using

t-expansion [i] based on digital (9, 46, 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]

(46−33, 46, 321)-Net over F₁₂₈ — Digital

Digital (13, 46, 321)-net over F₁₂₈, using

t-expansion [i] based on digital (12, 46, 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]

(46−33, 46, 45205)-Net in Base 128 — Upper bound on s

There is no (13, 46, 45206)-net in base 128, because

1 times m-reduction [i] would yield (13, 45, 45206)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 66765 068805 839088 839570 977353 930681 365379 779099 051975 399915 070005 366367 672044 551266 066678 663093 > 128⁴⁵ [i]