MinT - Best Known (45, 45+95, s)-Nets in Base 9

Best Known (45, 45+95, s)-Nets in Base 9

(45, 45+95, 81)-Net over F₉ — Constructive and digital

Digital (45, 140, 81)-net over F₉, using

t-expansion [i] based on digital (32, 140, 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]

(45, 45+95, 147)-Net over F₉ — Digital

Digital (45, 140, 147)-net over F₉, using

t-expansion [i] based on digital (43, 140, 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]

(45, 45+95, 1495)-Net in Base 9 — Upper bound on s

There is no (45, 140, 1496)-net in base 9, because

1 times m-reduction [i] would yield (45, 139, 1496)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 4 389803 382021 387774 694452 282224 469757 967776 703828 171373 138941 972729 606897 065382 851939 540907 898244 379228 265826 190819 109801 040352 628801 > 9¹³⁹ [i]