MinT - Best Known (34, 49, s)-Nets in Base 9

Best Known (34, 49, s)-Nets in Base 9

(34, 49, 400)-Net over F₉ — Constructive and digital

Digital (34, 49, 400)-net over F₉, using

9¹ times duplication [i] based on 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)

(34, 49, 1660)-Net over F₉ — Digital

Digital (34, 49, 1660)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(34, 49, 1476402)-Net in Base 9 — Upper bound on s

There is no (34, 49, 1476403)-net in base 9, because

1 times m-reduction [i] would yield (34, 48, 1476403)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 6362 704946 670754 628452 848239 863802 712288 493737 > 9⁴⁸ [i]