MinT - Best Known (141−97, 141, s)-Nets in Base 9

Best Known (141−97, 141, s)-Nets in Base 9

(141−97, 141, 81)-Net over F₉ — Constructive and digital

Digital (44, 141, 81)-net over F₉, using

t-expansion [i] based on digital (32, 141, 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]

(141−97, 141, 147)-Net over F₉ — Digital

Digital (44, 141, 147)-net over F₉, using

t-expansion [i] based on digital (43, 141, 147)-net over F₉, using
- net from sequence [i] based on digital (43, 146)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 43 and N(F) ≥ 147, using
    - a curve from the manYPoints database [i]

(141−97, 141, 1392)-Net in Base 9 — Upper bound on s

There is no (44, 141, 1393)-net in base 9, because

1 times m-reduction [i] would yield (44, 140, 1393)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 39 656849 778295 117744 719920 528784 676574 066759 657358 654673 552146 541149 501559 858568 365888 067877 572178 450904 962638 866662 704488 320228 569985 > 9¹⁴⁰ [i]