MinT - Best Known (56, 56+41, s)-Nets in Base 9

Best Known (56, 56+41, s)-Nets in Base 9

(56, 56+41, 344)-Net over F₉ — Constructive and digital

Digital (56, 97, 344)-net over F₉, using

1 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+41, 410)-Net over F₉ — Digital

Digital (56, 97, 410)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(56, 56+41, 39486)-Net in Base 9 — Upper bound on s

There is no (56, 97, 39487)-net in base 9, because

1 times m-reduction [i] would yield (56, 96, 39487)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 40 494579 679306 312676 720002 013818 763590 258283 023158 821707 858428 207872 142763 449419 486764 922721 > 9⁹⁶ [i]