MinT - Best Known (73−23, 73, s)-Nets in Base 3

Best Known (73−23, 73, s)-Nets in Base 3

(73−23, 73, 128)-Net over F₃ — Constructive and digital

Digital (50, 73, 128)-net over F₃, using

1 times m-reduction [i] based on digital (50, 74, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 37, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(73−23, 73, 172)-Net over F₃ — Digital

Digital (50, 73, 172)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(73−23, 73, 3247)-Net in Base 3 — Upper bound on s

There is no (50, 73, 3248)-net in base 3, because

1 times m-reduction [i] would yield (50, 72, 3248)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 22560 485311 183261 702869 676978 294977 > 3⁷² [i]