MinT - Best Known (38, 38+85, s)-Nets in Base 9

Best Known (38, 38+85, s)-Nets in Base 9

(38, 38+85, 81)-Net over F₉ — Constructive and digital

Digital (38, 123, 81)-net over F₉, using

t-expansion [i] based on digital (32, 123, 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]

(38, 38+85, 128)-Net over F₉ — Digital

Digital (38, 123, 128)-net over F₉, using

t-expansion [i] based on digital (33, 123, 128)-net over F₉, using
- net from sequence [i] based on digital (33, 127)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 33 and N(F) ≥ 128, using
    - a curve from the manYPoints database [i]

(38, 38+85, 1194)-Net in Base 9 — Upper bound on s

There is no (38, 123, 1195)-net in base 9, because

1 times m-reduction [i] would yield (38, 122, 1195)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 261 855867 435489 445389 583651 309151 062691 362653 130076 491335 121868 019285 564774 084008 423019 430801 966658 687060 213790 800625 > 9¹²² [i]