MinT - Best Known (149−97, 149, s)-Nets in Base 9

Best Known (149−97, 149, s)-Nets in Base 9

(149−97, 149, 81)-Net over F₉ — Constructive and digital

Digital (52, 149, 81)-net over F₉, using

t-expansion [i] based on digital (32, 149, 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]

(149−97, 149, 182)-Net over F₉ — Digital

Digital (52, 149, 182)-net over F₉, using

t-expansion [i] based on digital (50, 149, 182)-net over F₉, using
- net from sequence [i] based on digital (50, 181)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 50 and N(F) ≥ 182, using
    - a curve from the manYPoints database [i]

(149−97, 149, 2021)-Net in Base 9 — Upper bound on s

There is no (52, 149, 2022)-net in base 9, because

1 times m-reduction [i] would yield (52, 148, 2022)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1708 400747 715317 750626 090386 037019 716404 051169 878911 605468 909747 007608 582634 765644 257502 031553 072677 287891 983866 335127 198154 630384 685755 947777 > 9¹⁴⁸ [i]