MinT - Best Known (35, 132, s)-Nets in Base 9

Best Known (35, 132, s)-Nets in Base 9

(35, 132, 81)-Net over F₉ — Constructive and digital

Digital (35, 132, 81)-net over F₉, using

t-expansion [i] based on digital (32, 132, 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]

(35, 132, 128)-Net over F₉ — Digital

Digital (35, 132, 128)-net over F₉, using

t-expansion [i] based on digital (33, 132, 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]

(35, 132, 912)-Net in Base 9 — Upper bound on s

There is no (35, 132, 913)-net in base 9, because

1 times m-reduction [i] would yield (35, 131, 913)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 103279 137069 455571 725185 156458 176534 843885 004220 450998 619795 678481 240313 341692 733045 867622 666568 047693 927528 982634 613375 419265 > 9¹³¹ [i]