MinT - Best Known (62, 62+33, s)-Nets in Base 9

Best Known (62, 62+33, s)-Nets in Base 9

(62, 62+33, 448)-Net over F₉ — Constructive and digital

Digital (62, 95, 448)-net over F₉, using

3 times m-reduction [i] based on digital (62, 98, 448)-net over F₉, using
- trace code for nets [i] based on digital (13, 49, 224)-net over F₈₁, using
  - net from sequence [i] based on digital (13, 223)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 13 and N(F) ≥ 224, using
      - a function field by SÃ©mirat [i]

(62, 62+33, 1104)-Net over F₉ — Digital

Digital (62, 95, 1104)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(62, 62+33, 343250)-Net in Base 9 — Upper bound on s

There is no (62, 95, 343251)-net in base 9, because

1 times m-reduction [i] would yield (62, 94, 343251)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 499806 026605 537426 126636 466815 108416 077080 642837 343278 642098 420081 922474 898079 642786 426241 > 9⁹⁴ [i]