MinT - Best Known (123−50, 123, s)-Nets in Base 9

Best Known (123−50, 123, s)-Nets in Base 9

(123−50, 123, 344)-Net over F₉ — Constructive and digital

Digital (73, 123, 344)-net over F₉, using

9 times m-reduction [i] based on digital (73, 132, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 66, 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]

(123−50, 123, 599)-Net over F₉ — Digital

Digital (73, 123, 599)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(123−50, 123, 62994)-Net in Base 9 — Upper bound on s

There is no (73, 123, 62995)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2354 302906 801465 083246 136922 441275 690364 785686 443180 897467 889125 867645 479352 251320 338025 770372 186567 403882 424315 951321 > 9¹²³ [i]