MinT - Best Known (63, 63+83, s)-Nets in Base 9

Best Known (63, 63+83, s)-Nets in Base 9

(63, 63+83, 106)-Net over F₉ — Constructive and digital

Digital (63, 146, 106)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (5, 46, 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 (17, 100, 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]

(63, 63+83, 192)-Net over F₉ — Digital

Digital (63, 146, 192)-net over F₉, using

t-expansion [i] based on digital (61, 146, 192)-net over F₉, using
- net from sequence [i] based on digital (61, 191)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 61 and N(F) ≥ 192, using
    - Drinfeld modules of rank 1 [i]

(63, 63+83, 4756)-Net in Base 9 — Upper bound on s

There is no (63, 146, 4757)-net in base 9, because

1 times m-reduction [i] would yield (63, 145, 4757)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2 325811 093211 191899 333080 610051 165482 006656 397126 633073 931251 446897 326968 243716 074036 928644 707273 399211 684906 490431 120599 443632 080079 380969 > 9¹⁴⁵ [i]