MinT - Best Known (145−91, 145, s)-Nets in Base 9

Best Known (145−91, 145, s)-Nets in Base 9

(145−91, 145, 81)-Net over F₉ — Constructive and digital

Digital (54, 145, 81)-net over F₉, using

t-expansion [i] based on digital (32, 145, 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]

(145−91, 145, 182)-Net over F₉ — Digital

Digital (54, 145, 182)-net over F₉, using

t-expansion [i] based on digital (50, 145, 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]

(145−91, 145, 2465)-Net in Base 9 — Upper bound on s

There is no (54, 145, 2466)-net in base 9, because

1 times m-reduction [i] would yield (54, 144, 2466)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 261781 813056 499197 538187 039551 188717 056229 332043 302087 894809 900682 816161 774125 184600 824300 655608 577532 269723 855501 629561 388895 794169 596497 > 9¹⁴⁴ [i]