MinT - Best Known (150−97, 150, s)-Nets in Base 9

Best Known (150−97, 150, s)-Nets in Base 9

(150−97, 150, 81)-Net over F₉ — Constructive and digital

Digital (53, 150, 81)-net over F₉, using

t-expansion [i] based on digital (32, 150, 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]

(150−97, 150, 182)-Net over F₉ — Digital

Digital (53, 150, 182)-net over F₉, using

t-expansion [i] based on digital (50, 150, 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]

(150−97, 150, 2117)-Net in Base 9 — Upper bound on s

There is no (53, 150, 2118)-net in base 9, because

1 times m-reduction [i] would yield (53, 149, 2118)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15348 230905 885312 242250 816386 922022 809124 091756 137637 566383 523720 790997 174663 274571 527465 776368 338178 899037 111863 175305 732607 188334 561720 683265 > 9¹⁴⁹ [i]