MinT - Best Known (108−46, 108, s)-Nets in Base 9

Best Known (108−46, 108, s)-Nets in Base 9

(108−46, 108, 344)-Net over F₉ — Constructive and digital

Digital (62, 108, 344)-net over F₉, using

2 times m-reduction [i] based on digital (62, 110, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 55, 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]

(108−46, 108, 452)-Net over F₉ — Digital

Digital (62, 108, 452)-net over F₉, using

trace code for nets [i] based on digital (8, 54, 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]

(108−46, 108, 35644)-Net in Base 9 — Upper bound on s

There is no (62, 108, 35645)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 11 440117 448666 031927 159555 330764 783872 911179 734540 148954 727297 439398 471184 026376 039094 793381 263822 082969 > 9¹⁰⁸ [i]