MinT - Best Known (125−89, 125, s)-Nets in Base 9

Best Known (125−89, 125, s)-Nets in Base 9

(125−89, 125, 81)-Net over F₉ — Constructive and digital

Digital (36, 125, 81)-net over F₉, using

t-expansion [i] based on digital (32, 125, 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]

(125−89, 125, 128)-Net over F₉ — Digital

Digital (36, 125, 128)-net over F₉, using

t-expansion [i] based on digital (33, 125, 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]

(125−89, 125, 1027)-Net in Base 9 — Upper bound on s

There is no (36, 125, 1028)-net in base 9, because

1 times m-reduction [i] would yield (36, 124, 1028)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 21420 823646 227242 279806 899613 967364 351234 633024 505065 511812 512474 074237 147611 843893 610948 533368 143035 172421 634867 884673 > 9¹²⁴ [i]