MinT - Best Known (125−91, 125, s)-Nets in Base 9

Best Known (125−91, 125, s)-Nets in Base 9

(125−91, 125, 81)-Net over F₉ — Constructive and digital

Digital (34, 125, 81)-net over F₉, using

t-expansion [i] based on digital (32, 125, 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]

(125−91, 125, 128)-Net over F₉ — Digital

Digital (34, 125, 128)-net over F₉, using

t-expansion [i] based on digital (33, 125, 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]

(125−91, 125, 911)-Net in Base 9 — Upper bound on s

There is no (34, 125, 912)-net in base 9, because

1 times m-reduction [i] would yield (34, 124, 912)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 21842 378376 051294 768834 577998 041559 542172 923925 243541 365785 407349 756638 731473 879768 932564 367562 552736 786192 108850 093697 > 9¹²⁴ [i]