MinT - Best Known (38, 38+31, s)-Nets in Base 9

Best Known (38, 38+31, s)-Nets in Base 9

(38, 38+31, 232)-Net over F₉ — Constructive and digital

Digital (38, 69, 232)-net over F₉, using

3 times m-reduction [i] based on digital (38, 72, 232)-net over F₉, using
- trace code for nets [i] based on digital (2, 36, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(38, 38+31, 272)-Net over F₉ — Digital

Digital (38, 69, 272)-net over F₉, using

1 times m-reduction [i] based on digital (38, 70, 272)-net over F₉, using
- trace code for nets [i] based on digital (3, 35, 136)-net over F₈₁, using
  - net from sequence [i] based on digital (3, 135)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 3 and N(F) ≥ 136, using
      - a curve from the manYPoints database [i]

(38, 38+31, 16996)-Net in Base 9 — Upper bound on s

There is no (38, 69, 16997)-net in base 9, because

1 times m-reduction [i] would yield (38, 68, 16997)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 77416 652544 282148 576068 248349 188426 148192 119149 794822 452442 396441 > 9⁶⁸ [i]