MinT - Best Known (46, 46+57, s)-Nets in Base 9

Best Known (46, 46+57, s)-Nets in Base 9

(46, 46+57, 96)-Net over F₉ — Constructive and digital

Digital (46, 103, 96)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (5, 33, 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 (13, 70, 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]

(46, 46+57, 162)-Net over F₉ — Digital

Digital (46, 103, 162)-net over F₉, using

net from sequence [i] based on digital (46, 161)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 46 and N(F) ≥ 162, using
  - a curve from the manYPoints database [i]

(46, 46+57, 4210)-Net in Base 9 — Upper bound on s

There is no (46, 103, 4211)-net in base 9, because

1 times m-reduction [i] would yield (46, 102, 4211)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 21 582410 765587 157238 156156 701816 286410 251254 712682 436667 520574 845603 263930 089120 708493 235069 734817 > 9¹⁰² [i]