MinT - Best Known (104−65, 104, s)-Nets in Base 9

Best Known (104−65, 104, s)-Nets in Base 9

(104−65, 104, 81)-Net over F₉ — Constructive and digital

Digital (39, 104, 81)-net over F₉, using

t-expansion [i] based on digital (32, 104, 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]

(104−65, 104, 140)-Net over F₉ — Digital

Digital (39, 104, 140)-net over F₉, using

net from sequence [i] based on digital (39, 139)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 39 and N(F) ≥ 140, using
  - a curve from the manYPoints database [i]

(104−65, 104, 1865)-Net in Base 9 — Upper bound on s

There is no (39, 104, 1866)-net in base 9, because

1 times m-reduction [i] would yield (39, 103, 1866)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 195 848159 042210 647318 574367 195120 685224 777687 227194 476446 756508 657701 834511 937909 369937 229671 624193 > 9¹⁰³ [i]