MinT - Best Known (37, 66, s)-Nets in Base 9

Best Known (37, 66, s)-Nets in Base 9

(37, 66, 300)-Net over F₉ — Constructive and digital

Digital (37, 66, 300)-net over F₉, using

trace code for nets [i] based on digital (4, 33, 150)-net over F₈₁, using
- net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
    - a function field by SÃ©mirat [i]

(37, 66, 308)-Net over F₉ — Digital

Digital (37, 66, 308)-net over F₉, using

trace code for nets [i] based on digital (4, 33, 154)-net over F₈₁, using
- net from sequence [i] based on digital (4, 153)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 154, using
    - a curve from the manYPoints database [i]

(37, 66, 20351)-Net in Base 9 — Upper bound on s

There is no (37, 66, 20352)-net in base 9, because

1 times m-reduction [i] would yield (37, 65, 20352)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 106 124253 304316 212268 730889 664696 007605 982871 951303 543154 874369 > 9⁶⁵ [i]