MinT - Best Known (146−117, 146, s)-Nets in Base 9

Best Known (146−117, 146, s)-Nets in Base 9

(146−117, 146, 78)-Net over F₉ — Constructive and digital

Digital (29, 146, 78)-net over F₉, using

t-expansion [i] based on digital (22, 146, 78)-net over F₉, using
- net from sequence [i] based on digital (22, 77)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
    - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(146−117, 146, 110)-Net over F₉ — Digital

Digital (29, 146, 110)-net over F₉, using

t-expansion [i] based on digital (26, 146, 110)-net over F₉, using
- net from sequence [i] based on digital (26, 109)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 26 and N(F) ≥ 110, using
    - a curve from the manYPoints database [i]

(146−117, 146, 646)-Net in Base 9 — Upper bound on s

There is no (29, 146, 647)-net in base 9, because

1 times m-reduction [i] would yield (29, 145, 647)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2 374002 202092 912529 580773 058111 535903 332912 383486 369962 750271 350139 678204 854415 589933 390250 252143 527029 994620 435672 993823 573453 524186 642353 > 9¹⁴⁵ [i]