MinT - Best Known (47, 47+68, s)-Nets in Base 9

Best Known (47, 47+68, s)-Nets in Base 9

(47, 47+68, 81)-Net over F₉ — Constructive and digital

Digital (47, 115, 81)-net over F₉, using

t-expansion [i] based on digital (32, 115, 81)-net over F₉, using
- net from sequence [i] based on digital (32, 80)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
    - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(47, 47+68, 84)-Net in Base 9 — Constructive

(47, 115, 84)-net in base 9, using

2 times m-reduction [i] based on (47, 117, 84)-net in base 9, using
- base change [i] based on digital (8, 78, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(47, 47+68, 162)-Net over F₉ — Digital

Digital (47, 115, 162)-net over F₉, using

t-expansion [i] based on digital (46, 115, 162)-net over F₉, using
- net from sequence [i] based on digital (46, 161)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 46 and N(F) ≥ 162, using
    - a curve from the manYPoints database [i]

(47, 47+68, 2836)-Net in Base 9 — Upper bound on s

There is no (47, 115, 2837)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 54 889578 167013 255330 444022 749330 390737 842600 805271 067042 165433 404743 831253 730869 987649 047064 358005 587547 173905 > 9¹¹⁵ [i]