MinT - Best Known (47, 130, s)-Nets in Base 9

Best Known (47, 130, s)-Nets in Base 9

(47, 130, 81)-Net over F₉ — Constructive and digital

Digital (47, 130, 81)-net over F₉, using

t-expansion [i] based on digital (32, 130, 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, 130, 162)-Net over F₉ — Digital

Digital (47, 130, 162)-net over F₉, using

t-expansion [i] based on digital (46, 130, 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, 130, 2003)-Net in Base 9 — Upper bound on s

There is no (47, 130, 2004)-net in base 9, because

1 times m-reduction [i] would yield (47, 129, 2004)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1262 187561 084336 443873 996312 860501 126505 441248 811498 028473 445265 087503 704429 224252 558121 773967 177608 271442 990950 924720 296353 > 9¹²⁹ [i]