MinT - Best Known (45, 102, s)-Nets in Base 9

Best Known (45, 102, s)-Nets in Base 9

(45, 102, 94)-Net over F₉ — Constructive and digital

Digital (45, 102, 94)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (4, 32, 30)-net over F₉, using
  - net from sequence [i] based on digital (4, 29)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 4 and N(F) ≥ 30, using
      - a function field by SÃ©mirat [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]

(45, 102, 96)-Net in Base 9 — Constructive

(45, 102, 96)-net in base 9, using

base change [i] based on digital (11, 68, 96)-net over F₂₇, using
- net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
    - an explicitly constructive algebraic function field [i]

(45, 102, 147)-Net over F₉ — Digital

Digital (45, 102, 147)-net over F₉, using

t-expansion [i] based on digital (43, 102, 147)-net over F₉, using
- net from sequence [i] based on digital (43, 146)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 43 and N(F) ≥ 147, using
    - a curve from the manYPoints database [i]

(45, 102, 3891)-Net in Base 9 — Upper bound on s

There is no (45, 102, 3892)-net in base 9, because

1 times m-reduction [i] would yield (45, 101, 3892)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2 399658 473106 305452 812261 069792 654199 226064 668142 779423 908583 774019 260530 923296 045502 585453 439617 > 9¹⁰¹ [i]