MinT - Best Known (42−17, 42, s)-Nets in Base 9

Best Known (42−17, 42, s)-Nets in Base 9

(42−17, 42, 300)-Net over F₉ — Constructive and digital

Digital (25, 42, 300)-net over F₉, using

trace code for nets [i] based on digital (4, 21, 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]

(42−17, 42, 308)-Net over F₉ — Digital

Digital (25, 42, 308)-net over F₉, using

trace code for nets [i] based on digital (4, 21, 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]

(42−17, 42, 36562)-Net in Base 9 — Upper bound on s

There is no (25, 42, 36563)-net in base 9, because

1 times m-reduction [i] would yield (25, 41, 36563)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1330 336527 942505 786126 231512 325612 324545 > 9⁴¹ [i]