MinT - Best Known (32, 32+75, s)-Nets in Base 9

Best Known (32, 32+75, s)-Nets in Base 9

(32, 32+75, 81)-Net over F₉ — Constructive and digital

Digital (32, 107, 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]

(32, 32+75, 120)-Net over F₉ — Digital

Digital (32, 107, 120)-net over F₉, using

t-expansion [i] based on digital (31, 107, 120)-net over F₉, using
- net from sequence [i] based on digital (31, 119)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 31 and N(F) ≥ 120, using
    - a curve from the manYPoints database [i]

(32, 32+75, 969)-Net in Base 9 — Upper bound on s

There is no (32, 107, 970)-net in base 9, because

1 times m-reduction [i] would yield (32, 106, 970)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 142629 657969 646748 058837 403730 803369 891771 830257 875097 002023 974247 987157 390513 245772 631322 048996 030225 > 9¹⁰⁶ [i]