MinT - Best Known (142−95, 142, s)-Nets in Base 9

Best Known (142−95, 142, s)-Nets in Base 9

(142−95, 142, 81)-Net over F₉ — Constructive and digital

Digital (47, 142, 81)-net over F₉, using

t-expansion [i] based on digital (32, 142, 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]

(142−95, 142, 162)-Net over F₉ — Digital

Digital (47, 142, 162)-net over F₉, using

t-expansion [i] based on digital (46, 142, 162)-net over F₉, using
- net from sequence [i] based on digital (46, 161)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 46 and N(F) ≥ 162, using
    - a curve from the manYPoints database [i]

(142−95, 142, 1645)-Net in Base 9 — Upper bound on s

There is no (47, 142, 1646)-net in base 9, because

1 times m-reduction [i] would yield (47, 141, 1646)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 361 385775 199740 235493 623759 866351 633533 697255 884050 459121 026561 394160 670763 588241 426677 798860 472683 265050 951029 063955 083828 754052 589009 > 9¹⁴¹ [i]