MinT - Best Known (146−95, 146, s)-Nets in Base 9

Best Known (146−95, 146, s)-Nets in Base 9

(146−95, 146, 81)-Net over F₉ — Constructive and digital

Digital (51, 146, 81)-net over F₉, using

t-expansion [i] based on digital (32, 146, 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]

(146−95, 146, 182)-Net over F₉ — Digital

Digital (51, 146, 182)-net over F₉, using

t-expansion [i] based on digital (50, 146, 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]

(146−95, 146, 1989)-Net in Base 9 — Upper bound on s

There is no (51, 146, 1990)-net in base 9, because

1 times m-reduction [i] would yield (51, 145, 1990)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2 352284 791620 144429 844448 887044 604763 891536 915715 846790 091634 407206 334033 839362 625407 150255 180590 008246 170104 313825 897316 284970 847080 308241 > 9¹⁴⁵ [i]