MinT - Best Known (144−109, 144, s)-Nets in Base 9

Best Known (144−109, 144, s)-Nets in Base 9

(144−109, 144, 81)-Net over F₉ — Constructive and digital

Digital (35, 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]

(144−109, 144, 128)-Net over F₉ — Digital

Digital (35, 144, 128)-net over F₉, using

t-expansion [i] based on digital (33, 144, 128)-net over F₉, using
- net from sequence [i] based on digital (33, 127)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 33 and N(F) ≥ 128, using
    - a curve from the manYPoints database [i]

(144−109, 144, 849)-Net in Base 9 — Upper bound on s

There is no (35, 144, 850)-net in base 9, because

1 times m-reduction [i] would yield (35, 143, 850)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 30373 534154 557673 101709 618568 533065 229578 507209 217698 675220 373297 760748 900144 653993 546620 992889 231169 062220 107705 393187 086617 873422 195105 > 9¹⁴³ [i]