MinT - Best Known (161−47, 161, s)-Nets in Base 3

Best Known (161−47, 161, s)-Nets in Base 3

(161−47, 161, 228)-Net over F₃ — Constructive and digital

Digital (114, 161, 228)-net over F₃, using

1 times m-reduction [i] based on digital (114, 162, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 54, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

(161−47, 161, 403)-Net over F₃ — Digital

Digital (114, 161, 403)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(161−47, 161, 9807)-Net in Base 3 — Upper bound on s

There is no (114, 161, 9808)-net in base 3, because

1 times m-reduction [i] would yield (114, 160, 9808)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 21898 410158 907638 040884 680026 532094 020335 389625 503740 387023 302630 451009 285057 > 3¹⁶⁰ [i]