MinT - Best Known (45, 96, s)-Nets in Base 9

Best Known (45, 96, s)-Nets in Base 9

(45, 96, 102)-Net over F₉ — Constructive and digital

Digital (45, 96, 102)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (3, 28, 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, 68, 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]

(45, 96, 148)-Net over F₉ — Digital

Digital (45, 96, 148)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(45, 96, 5363)-Net in Base 9 — Upper bound on s

There is no (45, 96, 5364)-net in base 9, because

1 times m-reduction [i] would yield (45, 95, 5364)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 4 512002 700920 127640 230463 885324 034640 211884 800089 625733 229988 061063 478064 089871 056319 902881 > 9⁹⁵ [i]