MinT - Best Known (32, 145, s)-Nets in Base 9

Best Known (32, 145, s)-Nets in Base 9

(32, 145, 81)-Net over F₉ — Constructive and digital

Digital (32, 145, 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, 145, 120)-Net over F₉ — Digital

Digital (32, 145, 120)-net over F₉, using

t-expansion [i] based on digital (31, 145, 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, 145, 737)-Net in Base 9 — Upper bound on s

There is no (32, 145, 738)-net in base 9, because

1 times m-reduction [i] would yield (32, 144, 738)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 268888 265629 787816 680006 028686 170819 349725 416046 702877 885750 446871 060298 400770 822659 661690 443221 511995 149866 653293 180816 457095 497573 080705 > 9¹⁴⁴ [i]