MinT - Best Known (130−57, 130, s)-Nets in Base 9

Best Known (130−57, 130, s)-Nets in Base 9

(130−57, 130, 344)-Net over F₉ — Constructive and digital

Digital (73, 130, 344)-net over F₉, using

2 times m-reduction [i] based on digital (73, 132, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 66, 172)-net over F₈₁, using
  - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
      - a function field by SÃ©mirat [i]

(130−57, 130, 452)-Net over F₉ — Digital

Digital (73, 130, 452)-net over F₉, using

trace code for nets [i] based on digital (8, 65, 226)-net over F₈₁, using
- net from sequence [i] based on digital (8, 225)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 8 and N(F) ≥ 226, using
    - a curve from the manYPoints database [i]

(130−57, 130, 35159)-Net in Base 9 — Upper bound on s

There is no (73, 130, 35160)-net in base 9, because

1 times m-reduction [i] would yield (73, 129, 35160)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1252 057678 840923 558939 836303 208445 182223 970926 852874 708707 578399 136541 975229 301258 711433 704094 823416 657882 896303 414659 996417 > 9¹²⁹ [i]