MinT - Best Known (61, 61+46, s)-Nets in Base 9

Best Known (61, 61+46, s)-Nets in Base 9

(61, 61+46, 344)-Net over F₉ — Constructive and digital

Digital (61, 107, 344)-net over F₉, using

1 times m-reduction [i] based on digital (61, 108, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 54, 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]

(61, 61+46, 408)-Net over F₉ — Digital

Digital (61, 107, 408)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(61, 61+46, 32395)-Net in Base 9 — Upper bound on s

There is no (61, 107, 32396)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1 271024 475228 875366 086300 964994 349025 067032 877431 004064 965864 047127 527873 315396 818677 512756 429899 547169 > 9¹⁰⁷ [i]