MinT - Best Known (133−72, 133, s)-Nets in Base 9

Best Known (133−72, 133, s)-Nets in Base 9

(133−72, 133, 114)-Net over F₉ — Constructive and digital

Digital (61, 133, 114)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (8, 44, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]
2. digital (17, 89, 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]

(133−72, 133, 192)-Net over F₉ — Digital

Digital (61, 133, 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]

(133−72, 133, 5962)-Net in Base 9 — Upper bound on s

There is no (61, 133, 5963)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 8 221514 439612 558100 079018 944386 355148 722267 752181 473600 500845 508576 126122 482001 829029 825125 070014 747841 916599 657484 023430 242145 > 9¹³³ [i]