MinT - Best Known (11, 11+31, s)-Nets in Base 9

Best Known (11, 11+31, s)-Nets in Base 9

(11, 11+31, 40)-Net over F₉ — Constructive and digital

Digital (11, 42, 40)-net over F₉, using

t-expansion [i] based on digital (8, 42, 40)-net over F₉, using
- net from sequence [i] based on digital (8, 39)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
    - a function field by SÃ©mirat [i]

(11, 11+31, 55)-Net over F₉ — Digital

Digital (11, 42, 55)-net over F₉, using

net from sequence [i] based on digital (11, 54)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 11 and N(F) ≥ 55, using
  - a curve from the manYPoints database [i]

(11, 11+31, 316)-Net in Base 9 — Upper bound on s

There is no (11, 42, 317)-net in base 9, because

1 times m-reduction [i] would yield (11, 41, 317)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1330 919405 241871 242225 883412 260243 049817 > 9⁴¹ [i]