MinT - Best Known (125−55, 125, s)-Nets in Base 9

Best Known (125−55, 125, s)-Nets in Base 9

(125−55, 125, 344)-Net over F₉ — Constructive and digital

Digital (70, 125, 344)-net over F₉, using

1 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]

(125−55, 125, 414)-Net over F₉ — Digital

Digital (70, 125, 414)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(125−55, 125, 32926)-Net in Base 9 — Upper bound on s

There is no (70, 125, 32927)-net in base 9, because

1 times m-reduction [i] would yield (70, 124, 32927)-net in base 9, but
- 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]