MinT - Best Known (132−93, 132, s)-Nets in Base 9

Best Known (132−93, 132, s)-Nets in Base 9

(132−93, 132, 81)-Net over F₉ — Constructive and digital

Digital (39, 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]

(132−93, 132, 140)-Net over F₉ — Digital

Digital (39, 132, 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]

(132−93, 132, 1145)-Net in Base 9 — Upper bound on s

There is no (39, 132, 1146)-net in base 9, because

1 times m-reduction [i] would yield (39, 131, 1146)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 101672 086425 767634 018608 091423 450276 403449 192338 793968 787785 687567 862309 167320 012943 023114 727159 581452 191137 230278 486750 894241 > 9¹³¹ [i]