MinT - Best Known (69−23, 69, s)-Nets in Base 9

Best Known (69−23, 69, s)-Nets in Base 9

(69−23, 69, 344)-Net over F₉ — Constructive and digital

Digital (46, 69, 344)-net over F₉, using

9 times m-reduction [i] based on digital (46, 78, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 39, 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]

(69−23, 69, 1124)-Net over F₉ — Digital

Digital (46, 69, 1124)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(69−23, 69, 486264)-Net in Base 9 — Upper bound on s

There is no (46, 69, 486265)-net in base 9, because

1 times m-reduction [i] would yield (46, 68, 486265)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 77357 048945 170425 427842 688881 352601 072607 785140 190575 070390 355033 > 9⁶⁸ [i]