MinT - Best Known (55, 102, s)-Nets in Base 9

Best Known (55, 102, s)-Nets in Base 9

(55, 102, 300)-Net over F₉ — Constructive and digital

Digital (55, 102, 300)-net over F₉, using

trace code for nets [i] based on digital (4, 51, 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]

(55, 102, 308)-Net over F₉ — Digital

Digital (55, 102, 308)-net over F₉, using

trace code for nets [i] based on digital (4, 51, 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]

(55, 102, 18256)-Net in Base 9 — Upper bound on s

There is no (55, 102, 18257)-net in base 9, because

1 times m-reduction [i] would yield (55, 101, 18257)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2 393528 026784 905503 484004 198391 418532 358068 313272 366532 878840 250416 078520 662431 461838 344483 036537 > 9¹⁰¹ [i]