MinT - Best Known (143−97, 143, s)-Nets in Base 9

Best Known (143−97, 143, s)-Nets in Base 9

(143−97, 143, 81)-Net over F₉ — Constructive and digital

Digital (46, 143, 81)-net over F₉, using

t-expansion [i] based on digital (32, 143, 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]

(143−97, 143, 162)-Net over F₉ — Digital

Digital (46, 143, 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]

(143−97, 143, 1529)-Net in Base 9 — Upper bound on s

There is no (46, 143, 1530)-net in base 9, because

1 times m-reduction [i] would yield (46, 142, 1530)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3277 500234 141517 593646 429575 629630 555132 055091 080589 165776 065911 712630 249416 434824 184873 573564 979032 709195 410709 329475 845576 058396 196097 > 9¹⁴² [i]