MinT - Best Known (53, 148, s)-Nets in Base 9

Best Known (53, 148, s)-Nets in Base 9

(53, 148, 81)-Net over F₉ — Constructive and digital

Digital (53, 148, 81)-net over F₉, using

t-expansion [i] based on digital (32, 148, 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]

(53, 148, 182)-Net over F₉ — Digital

Digital (53, 148, 182)-net over F₉, using

t-expansion [i] based on digital (50, 148, 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]

(53, 148, 2187)-Net in Base 9 — Upper bound on s

There is no (53, 148, 2188)-net in base 9, because

1 times m-reduction [i] would yield (53, 147, 2188)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 191 157010 777484 151196 018378 892621 987968 351997 544003 535803 917845 420409 860401 984497 087809 198930 860907 398112 516112 967520 210005 038192 717881 896225 > 9¹⁴⁷ [i]