MinT - Best Known (144−97, 144, s)-Nets in Base 9

Best Known (144−97, 144, s)-Nets in Base 9

(144−97, 144, 81)-Net over F₉ — Constructive and digital

Digital (47, 144, 81)-net over F₉, using

t-expansion [i] based on digital (32, 144, 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]

(144−97, 144, 162)-Net over F₉ — Digital

Digital (47, 144, 162)-net over F₉, using

t-expansion [i] based on digital (46, 144, 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]

(144−97, 144, 1602)-Net in Base 9 — Upper bound on s

There is no (47, 144, 1603)-net in base 9, because

1 times m-reduction [i] would yield (47, 143, 1603)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 29470 425417 584688 284043 100883 388728 576811 213276 981221 679769 691822 228461 371207 902552 502691 580904 191823 424193 594411 516193 901993 551868 379265 > 9¹⁴³ [i]