MinT - Best Known (88−45, 88, s)-Nets in Base 9

Best Known (88−45, 88, s)-Nets in Base 9

(88−45, 88, 104)-Net over F₉ — Constructive and digital

Digital (43, 88, 104)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (8, 30, 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 (13, 58, 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]

(88−45, 88, 163)-Net over F₉ — Digital

Digital (43, 88, 163)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(88−45, 88, 6706)-Net in Base 9 — Upper bound on s

There is no (43, 88, 6707)-net in base 9, because

1 times m-reduction [i] would yield (43, 87, 6707)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 104636 077220 402632 752845 268727 873846 447193 361286 102532 378460 557283 604718 193096 754065 > 9⁸⁷ [i]