MinT - Best Known (88−38, 88, s)-Nets in Base 9

Best Known (88−38, 88, s)-Nets in Base 9

(88−38, 88, 320)-Net over F₉ — Constructive and digital

Digital (50, 88, 320)-net over F₉, using

2 times m-reduction [i] based on digital (50, 90, 320)-net over F₉, using
- trace code for nets [i] based on digital (5, 45, 160)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
      - a function field by SÃ©mirat [i]

(88−38, 88, 380)-Net over F₉ — Digital

Digital (50, 88, 380)-net over F₉, using

trace code for nets [i] based on digital (6, 44, 190)-net over F₈₁, using
- net from sequence [i] based on digital (6, 189)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 6 and N(F) ≥ 190, using
    - a curve from the manYPoints database [i]

(88−38, 88, 26036)-Net in Base 9 — Upper bound on s

There is no (50, 88, 26037)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 940690 441366 958905 663727 826733 812391 334478 484081 202604 491063 031513 978701 092153 569465 > 9⁸⁸ [i]