MinT - Best Known (84−43, 84, s)-Nets in Base 9

Best Known (84−43, 84, s)-Nets in Base 9

(84−43, 84, 102)-Net over F₉ — Constructive and digital

Digital (41, 84, 102)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (3, 24, 28)-net over F₉, using
  - net from sequence [i] based on digital (3, 27)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 3 and N(F) ≥ 28, using
      - the Hermitian function field over F₉ [i]
2. digital (17, 60, 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]

(84−43, 84, 156)-Net over F₉ — Digital

Digital (41, 84, 156)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(84−43, 84, 6398)-Net in Base 9 — Upper bound on s

There is no (41, 84, 6399)-net in base 9, because

1 times m-reduction [i] would yield (41, 83, 6399)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15 953853 156089 651934 881982 660695 783155 383216 052863 379048 159455 593004 912074 434393 > 9⁸³ [i]