MinT - Best Known (132−71, 132, s)-Nets in Base 9

Best Known (132−71, 132, s)-Nets in Base 9

(132−71, 132, 128)-Net over F₉ — Constructive and digital

Digital (61, 132, 128)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (13, 48, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]
2. digital (13, 84, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉ (see above)

(132−71, 132, 192)-Net over F₉ — Digital

Digital (61, 132, 192)-net over F₉, using

net from sequence [i] based on digital (61, 191)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 61 and N(F) ≥ 192, using
  - Drinfeld modules of rank 1 [i]

(132−71, 132, 6461)-Net in Base 9 — Upper bound on s

There is no (61, 132, 6462)-net in base 9, because

1 times m-reduction [i] would yield (61, 131, 6462)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 101603 397699 155095 560250 913893 438105 770505 976269 515150 248703 673563 398291 895567 091509 600902 921557 193263 018294 871446 794009 299089 > 9¹³¹ [i]