MinT - Best Known (101−53, 101, s)-Nets in Base 9

Best Known (101−53, 101, s)-Nets in Base 9

(101−53, 101, 106)-Net over F₉ — Constructive and digital

Digital (48, 101, 106)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (5, 31, 32)-net over F₉, using
  - net from sequence [i] based on digital (5, 31)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 5 and N(F) ≥ 32, using
      - a function field by GarcÃa and Quoos [i]
2. digital (17, 70, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(101−53, 101, 163)-Net over F₉ — Digital

Digital (48, 101, 163)-net over F₉, using

net from sequence [i] based on digital (48, 162)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 48 and N(F) ≥ 163, using
  - Drinfeld modules of rank 1 [i]

(101−53, 101, 6155)-Net in Base 9 — Upper bound on s

There is no (48, 101, 6156)-net in base 9, because

1 times m-reduction [i] would yield (48, 100, 6156)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 266265 709088 110161 412031 057730 588963 142306 700786 188567 640188 329016 499787 460442 063878 981834 435393 > 9¹⁰⁰ [i]