MinT - Best Known (56, 56+35, s)-Nets in Base 9

Best Known (56, 56+35, s)-Nets in Base 9

(56, 56+35, 344)-Net over F₉ — Constructive and digital

Digital (56, 91, 344)-net over F₉, using

7 times m-reduction [i] based on digital (56, 98, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 49, 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]

(56, 56+35, 623)-Net over F₉ — Digital

Digital (56, 91, 623)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(56, 56+35, 101084)-Net in Base 9 — Upper bound on s

There is no (56, 91, 101085)-net in base 9, because

1 times m-reduction [i] would yield (56, 90, 101085)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 76 185947 341409 865696 740408 749151 467234 055978 127852 490260 973713 439436 186964 215097 293673 > 9⁹⁰ [i]