MinT - Best Known (33, 48, s)-Nets in Base 9

Best Known (33, 48, s)-Nets in Base 9

(33, 48, 400)-Net over F₉ — Constructive and digital

Digital (33, 48, 400)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (9, 16, 200)-net over F₉, using
  - trace code for nets [i] based on digital (1, 8, 100)-net over F₈₁, using
    - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
        a function field by SÃ©mirat [i]
2. digital (17, 32, 200)-net over F₉, using
  - trace code for nets [i] based on digital (1, 16, 100)-net over F₈₁, using
    - net from sequence [i] based on digital (1, 99)-sequence over F₈₁ (see above)

(33, 48, 1420)-Net over F₉ — Digital

Digital (33, 48, 1420)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(33, 48, 1078658)-Net in Base 9 — Upper bound on s

There is no (33, 48, 1078659)-net in base 9, because

1 times m-reduction [i] would yield (33, 47, 1078659)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 706 967572 368672 203796 459176 568788 641353 396265 > 9⁴⁷ [i]