MinT - Best Known (39, 39+24, s)-Nets in Base 9

Best Known (39, 39+24, s)-Nets in Base 9

(39, 39+24, 344)-Net over F₉ — Constructive and digital

Digital (39, 63, 344)-net over F₉, using

1 times m-reduction [i] based on digital (39, 64, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 32, 172)-net over F₈₁, using
  - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
      - a function field by SÃ©mirat [i]

(39, 39+24, 496)-Net over F₉ — Digital

Digital (39, 63, 496)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(39, 39+24, 67608)-Net in Base 9 — Upper bound on s

There is no (39, 63, 67609)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1 310196 898143 283876 777678 592082 299539 801210 684465 713363 198945 > 9⁶³ [i]