MinT - Best Known (72−43, 72, s)-Nets in Base 9

Best Known (72−43, 72, s)-Nets in Base 9

(72−43, 72, 78)-Net over F₉ — Constructive and digital

Digital (29, 72, 78)-net over F₉, using

t-expansion [i] based on digital (22, 72, 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]

(72−43, 72, 110)-Net over F₉ — Digital

Digital (29, 72, 110)-net over F₉, using

t-expansion [i] based on digital (26, 72, 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]

(72−43, 72, 1814)-Net in Base 9 — Upper bound on s

There is no (29, 72, 1815)-net in base 9, because

1 times m-reduction [i] would yield (29, 71, 1815)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 57 022251 564299 751534 477380 290908 132508 188748 978137 009745 618053 714201 > 9⁷¹ [i]