MinT - Best Known (70, 70+54, s)-Nets in Base 9

Best Known (70, 70+54, s)-Nets in Base 9

(70, 70+54, 344)-Net over F₉ — Constructive and digital

Digital (70, 124, 344)-net over F₉, using

2 times m-reduction [i] based on digital (70, 126, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 63, 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]

(70, 70+54, 452)-Net over F₉ — Digital

Digital (70, 124, 452)-net over F₉, using

trace code for nets [i] based on digital (8, 62, 226)-net over F₈₁, using
- net from sequence [i] based on digital (8, 225)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 8 and N(F) ≥ 226, using
    - a curve from the manYPoints database [i]

(70, 70+54, 32926)-Net in Base 9 — Upper bound on s

There is no (70, 124, 32927)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 21192 608988 395690 480612 774353 942879 425692 851591 415042 537426 428601 590515 149505 594809 877018 667862 369600 706693 384400 157225 > 9¹²⁴ [i]