MinT - Best Known (46, 99, s)-Nets in Base 9

Best Known (46, 99, s)-Nets in Base 9

(46, 99, 102)-Net over F₉ — Constructive and digital

Digital (46, 99, 102)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (3, 29, 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, 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]

(46, 99, 162)-Net over F₉ — Digital

Digital (46, 99, 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, 99, 5195)-Net in Base 9 — Upper bound on s

There is no (46, 99, 5196)-net in base 9, because

1 times m-reduction [i] would yield (46, 98, 5196)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3282 939897 733811 989108 804489 981491 991418 255037 506221 888859 496131 519567 684890 831330 373959 632705 > 9⁹⁸ [i]