MinT - Best Known (82−36, 82, s)-Nets in Base 9

Best Known (82−36, 82, s)-Nets in Base 9

(82−36, 82, 320)-Net over F₉ — Constructive and digital

Digital (46, 82, 320)-net over F₉, using

trace code for nets [i] based on digital (5, 41, 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]

(82−36, 82, 334)-Net over F₉ — Digital

Digital (46, 82, 334)-net over F₉, using

trace code for nets [i] based on digital (5, 41, 167)-net over F₈₁, using
- net from sequence [i] based on digital (5, 166)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 167, using
    - a curve from the manYPoints database [i]

(82−36, 82, 20985)-Net in Base 9 — Upper bound on s

There is no (46, 82, 20986)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1 770172 203254 207685 008375 562928 927520 477824 724798 720315 517515 575280 061750 368865 > 9⁸² [i]