MinT - Best Known (47, 47+71, s)-Nets in Base 9

Best Known (47, 47+71, s)-Nets in Base 9

(47, 47+71, 81)-Net over F₉ — Constructive and digital

Digital (47, 118, 81)-net over F₉, using

t-expansion [i] based on digital (32, 118, 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+71, 82)-Net in Base 9 — Constructive

(47, 118, 82)-net in base 9, using

2 times m-reduction [i] based on (47, 120, 82)-net in base 9, using
- base change [i] based on digital (7, 80, 82)-net over F₂₇, using
  - net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
      - a function field by SÃ©mirat [i]

(47, 47+71, 162)-Net over F₉ — Digital

Digital (47, 118, 162)-net over F₉, using

t-expansion [i] based on digital (46, 118, 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+71, 2670)-Net in Base 9 — Upper bound on s

There is no (47, 118, 2671)-net in base 9, because

1 times m-reduction [i] would yield (47, 117, 2671)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 4450 200795 949549 714910 242719 627889 309091 433933 786758 215800 716261 809481 319184 673613 668100 766168 893906 665129 095017 > 9¹¹⁷ [i]