MinT - Best Known (125−61, 125, s)-Nets in Base 9

Best Known (125−61, 125, s)-Nets in Base 9

(125−61, 125, 200)-Net over F₉ — Constructive and digital

Digital (64, 125, 200)-net over F₉, using

1 times m-reduction [i] based on digital (64, 126, 200)-net over F₉, using
- trace code for nets [i] based on digital (1, 63, 100)-net over F₈₁, using
  - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]

(125−61, 125, 264)-Net over F₉ — Digital

Digital (64, 125, 264)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(125−61, 125, 13222)-Net in Base 9 — Upper bound on s

There is no (64, 125, 13223)-net in base 9, because

1 times m-reduction [i] would yield (64, 124, 13223)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 21227 642665 066863 373120 839433 235056 150085 603363 185614 491771 816163 145689 484794 337349 850932 107788 756615 199594 450366 723473 > 9¹²⁴ [i]